26

GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

� ��������� �

� � ����������� � ������� "!���� �#!$�%��� � �� �� �&!'

(*),+.-0/21435-06870+:9<;>=%9?70;.9@1:9@)A+4;[email protected]+.14+.-068+F=%9<;.9?G=P0+.6H/2)I9@JK=L/E+.-M+.-09 R����%(N( OO1.3N-09@PQ9PD6H1:9@J"GR),+.-09 D.OTSOB01./2)0UV1:WX)A+.-I9<+./23<6HCYCEWZUH9@)I9<;N68+:9@J[[email protected];N9@JKJ068+.6]\ J /E;51:+<^_=`9a3bGRPQ7D68;.9@J"+.-I97c9<;.deGH;NP6H)03b9@1fGHd�+.-I9 � Jhg � ^_CYPji � J_g � ^h6H)0J Vkg PQ9<+.-IG]J01<\ �M9l1.-IGm=�;.9@3bGR)01:+:;5B03b+./EGR)M;.9@1NB0CE+.1GHd�376QdnGH;J0/Eop9<;.9@)A+�Y5q��Hrts � Wvuxw W*rtw8qNY<yVzvsHu{q|w�Y~} �]� O���6H)0J�J0/Eop9<;.9@)A+j/2)0/E+./26HC%[email protected]@1$376 ! \ � 9@3bGR)0J�^;.9@3bGR)01.+:;NB03b+./EGR)a;.9@1NB0CE+.1`GHd73 6 deGH;kJ0/�oc9<;.9@)A+�)AB0P|Pc9<;N1%GHdh1:GRB0;N3b9bi�JI9<+:9@3b+:GH;L7t6H/E;N1�68;.9�70;.9@1:9@)A+:9@J�\�(v)6HJ0J0/2+./EGR)�^]=%9�1.-IGm=�6Q;.9@3bGR)01:+:;5B03b+./EGR)�9b�I6HPQ7DCE9fGHdT6PQ9@JD/2B0PO+.-068+L3bGR)A+.6H/2)I9@J�6Q�HGR/2J�;.9<UR/2GR)�\

� �5� � 3��-,j�������>3�� 3L��� �Z� �?��5��� � �M� �?��k�: ��� @ � /983B: �

Sk-I9ZP6H/2)'deGX3<BD1?GHd>GRBI;�1:+.B0J0W�=�6H1a+.-I9,3bGRPQ7D68;N/Y1:GR)�GHd>3bGRPQ7tBI+.68+./EGR)06HCf1:7c9<9@J�^�;.G8iPDB01.+.)[email protected]<^�6H)0J�6H3<3<B0;N6H3bW"GHd�+.-I9 � J_g � ^�CYPji � J_g � ^�6H)0J Vkg P9<+.-IGXJD1Q/2) �fSf\&Sk-I9<;.9<deGH;.9H^�=`93bGRPQ7D68;N9@J�+.-I9@1:9f+:9@35-0)0/2�XBI9@1�deGH;kJ0/�oc9<;.9@) +k1N/EUR)06HC�ix+:G8i�)IGR/Y1:9�;N68+./EGR1�[email protected];N9@PQ9@) +kJD68+.66H)0JdeGH;�JD/�op9<;N9@) +�/2)0/E+./26HC¡[email protected]:9@1@\�¢�68;5/EGRB01 �]� O£35-06H)IUH9j+.-I9Q68707c9@68;N6H)03b9>GHd�+.-I9>G=P C:9@3b+./E�H9jdeBD)03b+./EGR)6H)0J¤1NBIPD1:9@�XBI9@)A+.CEW"CE9@6HJ�+:GKJ0/�oc9<;.9@)A+Q;.9@3bGR)01:+:;5B03b+./EGR)�;.9@1NB0CE+.1<\ J BI;.+.-I9<;NPGH;.9H^`1.+.68;.+./2)IU,+.-09VGH7Ii+./2P/2¥@68+./EGR)¦70;.G][email protected]>dn;.GRP�J0/Eop9<;.9@)A+j/2)0/E+./26HC�[email protected]:9@1QP6mW"6HC21.GZC29@6HJ"+:GMJ0/Eop9<;.9@)A+>;.9@3bGR)01:+:;NBD3b+./EGR);[email protected]+.1<\kSk-I9�G=P C:9@3b+./E�H9�d{B0)03b+./2GR)~P6mW~-06@�H9Q6l1./2)IURC29FCEG]3<6HC¡P/2)D/2P�BDP�^IPDBI+�+.-I9>CY/2)I941:9@68;N35-§70;.G8i

¨ � H

Page 2: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � F ���Xs � u�ybz������ � ^ ybz q �Ns ��� y �NwHrTY u{z ��@u{q|w8r � y[Y � � u�Y

3b9<9@J01�GR)KJ0/Eop9<;.9@)A+47D68+.-D14+:Gm=�68;NJ01>+.-I9?P/2)0/2P>B0P +.-068+>3<6H)"C29@6HJ,+:G�6~70;.9@P68+.B0;.9+:9<;NP/Y)068+./EGR)/Ed�+.-I9 1.+:GH707D/2)IU�3b;N/E+:9<;N/EGR)K/21F1.68+./Y109@J�\ R~GH;.9<Gm�H9<;@^�/2d`+.-09 1:+.68;.+./2)0U~7cGR/2)A+4/214+:GXG~d{68;>6m=`6mW,de;.GRP+.-I9j+:;NBI9j1:GRC2B0+./EGR)�^p+.-I9Q�AB06HJ0;N68+./23>PQGXJ09@ChP 6@W�)0GH+aPc9j6 UHGXG]JM687070;.Gm�]/2P 68+./EGR)~GHd%+.-I9jG=P C:9@3b+./E�H9d{B0)03b+./EGR)�\ V GR)D1:9@�AB09@) +.CEWH^D+.-I94C2/2)I9f1:9@68;53N-~J0GA9@1k)0GH+k70;.G]3b9<9@J�+:Gm=�68;NJ01L+.-I9FP/Y)0/2P>B0P�68+�6HC2C|\

� ���-��� �Q3'�� D>(��� ��� %�����<6 ) 9 ;=� %'/�29

P )K9b�]6HP7DCE9GHdk6�1.3<68+:+:9<;N/2)IU§PQ9@J0/2BDP /21F1N-IGm=L)"/2) J /EURBI;N9 �A\ ¨ \VSk-I9l3b;.GR1.1vi�1:9@3b+./2GR)06HC/2P68UH9�+:G`Pc9a;.9@3bGR)01.+:;NB03b+:9@J¤3bGR)01N/21:+:9@J[GHd�+.-I;.9<9aG=P C:9@3b+.1=L/E+.-[1.3<68+:+:9<;5/2)IU,3bGX9�� 3</E9@)A+.1QGHd 3$#����� M�3<P � & ^ 3$#��!a � �~3<P � & ^&6H)0J 3$#�� ¨H¨�� F�3<P � & ^T=L-0/Y3N-M=`9<;.9l9@P<Pc9@J0JI9@JK/2)K6��~3<P � �~3<PPD6H34LAUH;.GRBD)0J,PQ9@J0/YB0P�=L/E+.- 3$#�� H � a�3<P � & \Sk-I967Pt1:GH;.70+./EGR)M3bGX9�� 3</E9@)A+ 3 � � ��� � H 3<P � & J0/2J)IGH+�� 68;NW�=L/E+.-0/2)V+.-I9>/Y1:GH+:;.GH7D/23<6HCYCEW�1.3<68+:+:9<;N/2)IUaPQ9@J0/YB0P }�#�� � �5\�Sk-I9�UH9@)I9<;N6HCT3N-068;56H3b+:9<;fGHd�+.-I9G=P C:9@3b+./E�H94d{B0)03b+./EGR)a7D;N/2P68;N/YCEWJI9<7c9@)0J01�GR)�+.-09FJ068+.6Q+ WA7c94B01:9@J"}e9H\ UI\%J068+.6/Y)a+.-I94+./2PQ94J0GRP6H/2)�^de;.9@�AB09@)03bWKJIGRP6H/Y)�^&GH;Q/2)K+.-09a3bGR)A+./2)XBIGRB01>=�6@�H9VJIGRP6H/Y)t� � � 3N-A=%9@/EUH9<;�M�M��x^ 6H)0J[/21>/2)0J09<7p9@)DJI9@) +GHdF+.-09M7D- W]1./23<6HC�70;.GH7c9<;.+./29@1?GHd�+.-I9Z+./21.1.B09bi�C2/ LH9ZPQ9@J0/2B0PV\ Sk-I9<;.9<deGH;.9H^�� 68;N/2GRB01l9b�]6HPQ7tCE9@1l=L/E+.-J0/�oc9<;.9@)A+�GH7D+./23<6HC¡7t68;N6HPQ9<+:9<;N1�=L/YC2C�)IGH+fCE9@6HJ�+:GadeB0)DJ06HPQ9@)A+.6HC2CEW�J0/�oc9<;.9@)A+�;.9@1NB0CE+.1<^c6H)0J�+.-I9Q1.6HPQ91:+.B0J0W§3bGRB0CYJM6HC21:G~-06m�H9oPc9<9@),3<68;.;5/E9@JZGRBI+4deGH;F6H)0/21.GH+:;.GH7D/23<6HC2C2W�1.3<68+:+:9<;N/Y)IU~PQ9@J0/Y6aGH;FdeGH;4� 68;5/EGRB0167PD1:GH;N70+./EGR)�3bGX9�� 3</E9@)A+.1<\$(v)0JI9<9@J�=%9§-06@�H9Z1./2P>B0C268+:9@J¤JD/�op9<;N9@) ++ WA7c9@1?GHd4PQ9@J0/26Z+.-D68+?�868;.W�/2)67PD1:GH;N70+./EGR),6H)0JK1.3<68+:+:9<;N/2)IU~70;.GH7c9<;.+./E9@1<\?Sk-I9Q;[email protected]+.1f=`9<;.9 �XB06HC2/E+.68+./E�H9@C2W�+.-I9?1.6HPQ9?6H1FdnGH;F+.-068+70;[email protected]@) +:9@JV/Y)a+.-0/21�9b�I6HPQ7DCE9H\

Sk-I94PQ9@JD/2B0P =�6H1�1.B0;.;.GRB0)0J09@JiPXW aj9@�XB06HC2CEWa1:7D6H3b9@J�1:GRBI;N3b9@1�6H)0J ¨H¨ F9@�AB06HCYCEWl1.7D6H3b9@JJI9<+:9@3b+:GH;N1@\ � 1:GRBI;N3b9@1�6H)0J � M~JI9<+:9@3b+:GH;N1�=%9<;N9 7DC26H3b9@JKGR),9@6H35-"1./YJI9QGHd�+.-I9 PQ9@JD/2B0P�\ � 9<+:9@3b+:GH;;.9@6HJ0/Y)IUR1�GR)M+.-I9Q1.6HPQ91./YJI9>6H14+.-I9Q1:GRBI;N3b9H^�=`9<;.9)IGH+4BD1:9@J§dnGH;f+.-I9Q;N9@3bGR)01:+:;NB03b+./2GR)�\ 9@)03b9H^�=`9G=P0+.6H/2)09@J"6~+:GH+.6HC%GHd�a � a��~1.GRBI;N3b9bi�JI9<+:9@3b+:GH;Q7D6H/2;N1<\[email protected];.9@J¦J068+.6§68+�+.-09lJI9<+:9@3b+:GH;j7cG8i1./E+./2GR)01F=`9<;.9aUH9@)I9<;N68+:9@JePXW"BD1./2)IU�+.-I9l3bGH;N;.9@3b+1:7D68+./26HC�J0/Y1:+:;N/1PDB0+./EGR)ZGHdLGH70+./Y3<6HC%7D;.GH7c9<;.+./E9@1a}{1:9<9J /EURBI;.9 �A\ ¨ �5\ Sk-I9�dnGH;N=`68;NJ'3<6HC23<BDC268+./EGR)01?=%9<;N9§7c9<;.deGH;NPQ9@J�GR)'6 F ¨ � F ¨ UH;N/2J =L/E+.- ¨ F"GH;NJ0/�i

Page 3: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs � u�ybz������ � ^ ybz q �Ns ��� y �NwHrTY u{z ��@u{q|w8r � y[Y � � u�Y ¨ � �

7��

� �� � ��� �

J /EURBI;.9��A\ ¨� � 3<68+:+:9<;5/2)IUV3bGX9�� 3</E9@)A+.1 376�GHd`GH;N/EUR/2)06HChPQ9@J0/YB0P�=L/E+.-ZJ0/2PQ9@)D1./EGR)01�GHd �a3<P � �a3<P3bGR)A+.6H/2)0/2)IUj+.-I;N9<9�-09<+:9<;.GHUH9@)I9@/E+./E9@14} 3 # � ��� Mj3<P � & ^ 3 # � a � �>3<P � & ^06H)0J�3 # � ¨H¨�� Fj3<P � & �5\�Sk-I9PDB0C L?PQ9@J0/YB0P -06HJV61.3<68+:+:9<;5/2)IU 3bGX9�� 3</E9@)A+kGHd 3$# � H � a 3<P � & \)068+:9@1aPXW~B01./2)0U +.-I9 D)0/E+:9bi�JD/�op9<;N9@)03b9FJ0/21N3b;.9<+:9bixGH;NJ0/2)D68+:9@1�P9<+.-IGXJkPD6H1:9@J§GR)§+.-I9D.OTSf\ �M9QB01:9@J7D68;.+.C2WQ;.9�09@3b+./E�H9yPcGRB0)0J068;NWj3bGR)DJ0/E+./EGR)01 PD6H1:9@JlGR) J ;.9@1N)I9@C � 1�C26@='=L/2+.-?6>-IGRPQGHUH9@)I9<GRBD1�;.9<dn;56H3b+./E�H9/2)0J09b��� � ¨�� H �KdeGH;+.-I9~1N3<68+:+:9<;N/2)IUKP9@J0/2B0P�\�Sk-09V1:WX)A+.-I9<+./23�[email protected];.9@PQ9@)A+ J068+.6,=%9<;.9�B01:9@J+:G~;N9@3bGR)01:+:;NB03b+>6H)K/2P 68UH9 GHd�+.-I9?JD/21:+:;N/1PtBI+./EGR)�GHd 376b\�Sk-I9;.9@3bGR)D1:+:;NB03b+./EGR)K70;.G][email protected]=�6H14+:9<;5P/�i)068+:9@JZ68de+:9<;f+.-I9�;N9@C268+./E�H9jJ0/�oc9<;.9@)03b9 % }�� M � & : � M ����� M % GHd +.-I9jG=P��v9@3b+./2�H9�d{B0)03b+./EGR)kPc9<+�=`9<9@)Z+�=`G1.BIPt1:9@�AB09@) +>/E+:9<;N68+./EGR)¦1:+:9<7D1��K6H)0J�}���� ¨ �F=�6H1j1.P6HC2CE9<;�+.-06H)�� � ¨ � ��� \�SL-0/2141:+:GH7D7D/2)IU§3b;N/E+:9bi;N/EGR)§;.9<7tC26H3b9@J§+.-I9Q3b;N/E+:9<;N/EGR) ���f} � M � ! ��6H1FPQ9@) +./2GR)I9@JZ/2) � BIPD1:9@3b+./EGR)#"X\ � \ �I\jSk-I9>UH;N6HJ0/E9@)A+���f} � M �>3bGR) +.6H/2)09@J¤�H9<;.W[C268;.UH9V�86HC2BI9@1 /2)[70;.Gm�]/2P /E+�W"+:GK1:GRBI;N3b9~7pGR1N/E+./EGR)01<^ =L-0/235-�3bGR) +:;N/>PDBI+:9@JPQGH;.9l+:G§+.-I9 G �H9<;N6HC2C�)IGH;NP ���f} � M � +.-06H)"+.-I9l;.9@P6H/2)0/Y)IU��H9@3b+:GH;Q9@CE9@PQ9@)A+.1<\ZSk-I9<;.9<deGH;.9H^T+.-I93bGR)0J0/2+./EGR) % }�� M � & : � M ����� M %$ �k687D7p9@68;51�+:GoPc9yPp9<+:+:9<;�1.B0/E+:9@JadeGH;kGRBI;�68707DC2/23<68+./2GR)01<\

� ���-��� ����%D) #&%'#(��) �-,'&E� 6)(-� � � � ��3'6 �$*+IGH;l9<� 6HC2BD68+./2)IUM+.-I9§/2P68UH9~6H3<3<BI;56H3bW¤GHd�+.-I9~;.9@3bGR)D1:+:;NB03b+:9@J /2P68UH9@1<^�=`9~JI9<+:9<;NP /2)I9@J

+.-I9 �5w8z z:y � sHu{q|w8r �Nwmy , �<qxybrDu % 4�R � : ¨ � ¨ �TGHdT+.-I94;.9@3bGR)D1:+:;NB03b+:9@J§/2P68UH9F6H)DJV+.-I94GH;5/EUR/2)06HC�P9@J0/2B0P}e+.68;.UH9<+�/2P68UH9 �5\%SL-0/21�3bGA9��?3</E9@) +�/21kJI9 D)09@J�6H1 � -�;[email protected]/. � �

% 4 � =1032 4N } 365 6 � :87365 6 �b} 369 6 � :87369 6 �}e(;:�� : ¨ �=< 3 5 6 < 3 9 6 � }�>A\ ¨ �

Page 4: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨���� ���Xs��cu�ybz������ �� ybz q�Ns ��� y�NwHr� u{z ��@u{q|w8r � y� � � u� =L-I9<;N9L+.-I9� uxs8r��Rs8z����Ay��mq|sHu{q|w8r�<$3 9 6 GHd�+.-I9�+.68;.UH9<+kPQ9@JD/2B0P�6H)DJ +.-I9�1:+.6H)0JD68;NJ?J09<�X/268+./2GR) <$3 5 6 GHd+.-I94;N9@3bGR)01:+:;NB03b+:9@J~/2P68UH9F68;.9FUR/E�H9@)dPXW

<$3 9 6 � ���� ¨(;:�� : ¨ 032 4�

N } 3 9 6 � :873 9 6 � � }�>A\ � �6H)0J

< 3 5 6 � ���� ¨( :�� : ¨ 032 4�

N } 3 5 6 � : 73 5 6 � � � }�>A\��R�Sk-I9Q/2)DJI9b��/�R�� ¨! ( : �!"�3bGR)01:+./2+.BI+:9@1fGR)I9j7D/��]9@ChGHd +.-I9/YP68UH9jGH;fGR)I9Q9@CE9@PQ9@)A+fGHd +.-I9Q�H9@3b+:GH; � 6<^;.9@1:7c9@3b+./E�H9@C2WH\TSL-I9k�ABD6H) +./E+./29@1 73 9 6 6H)0J 73 5 6 /2)DJ0/23<68+:9�+.-I9#� y.sHr$� s!% �Dy& TGHdtGH70+./Y3<6HCI7D68;N6HPQ9<+:9<;51�GHdc+.-I9+.68;.UH9<+F/YP68UH96H)0JZ+.-I9Q;.9@3bGR)D1:+:;NB03b+:9@J,/YP68UH9H^¡;[email protected]@3b+./2�H9@CEWH\('OC268;.UH9Q�86HC2BI9jGHd % 4?1.-IGm=�1f6�-0/EUR-3bGH;.;.9@CY68+./EGR)[Pc9<+�=`9<9@)Z+.-I9j;.9@3bGR)01:+:;NBD3b+:9@JM6H)0JZ+.-I9j+.68;.UH9<+4/2P68UH9Q6H)0JM/Y)0J0/23<68+:9@1�6a;.9@3bGR)01:+:;5B03b+:9@J/2P68UH9�=L/2+.-?-0/2UR-l6H3<3<B0;N6H3bWH\)'�C2PQGR1:+�)IGQ3bGH;.;.9@CY68+./EGR)fPp9<+ =%9<9@)a+.-09�+.68;NUH9<+L6H)0Jl+.-I9�;.9@3bGR)01:+:;5B03b+:9@J/2P68UH9�/21�dnGRBD)0J�/Ed % 4F/21k�H9<;.W�1.P6HC2C|\

*`9@1./2JI9@1�+.-I943bGH;N;.9@C268+./EGR)V3bGX9�� 3</E9@)A+ % 4H^I=%9�6HC21:GJI9 D)09�6+�Ay��mq|sHu{q|w8r-,bs.@uxw8z %0/ R1� � �2 �6H1 �

%0/ �43 ¨ �]}e( :��A� = 032 4N } 3 5 6 � : 3 9 6 � � �<$3 9 6 � }�>A\65A�

Sk-0/Y1�7D68;N6HPQ9<+:9<;j/2146�[email protected];.9 GHd`+.-09?JI9<�]/268+./EGR)MGHd�+.-I9 ;.9@3bGR)01:+:;NBD3b+:9@J"/2P 68UH9dn;NGRP +.-I9+.68;NUH9<+/2P68UH9H\�(*+�/21�JI9 D)09@J�6H1�+.-I9>;N68+./EGlGHd&+.-I9 ��i�1.�XB068;.9>9<;.;.GH;f)IGH;NPV^t=L-D/23N-~=`6H1�G=P0+.6H/2)09@J~de;.GRP�+.-I9+.68;.UH9<+F6H)DJ�;N9@3bGR)01:+:;NB03b+:9@JK/2P68UH9H^¡6H)0J§+.-I91.+.6H)0J068;NJZJI9<�]/268+./EGR)ZGHd%+.-I9Q+.68;.UH9<+4/2P68UH9H\-'�1NP6HC2C�86HC2BI94GHd %7/ /2)0J0/Y3<68+:9@1k6;.9@3bGR)D1:+:;NB03b+:9@J§/2P68UH9�=L/E+.-V-0/2UR-V6H3<3<BI;N6H3bWH\LSL-I9F3bGH;.;.9@CY68+./EGR)~3bGX9�� 3</E9@)A+6H)0JK+.-I9 JI9<�]/268+./EGR)Kde6H3b+:GH;>GHdk6HC2C&;.9@3bGR)D1:+:;NB03b+:9@J¦/2P68UH9@1FGHd�+.-I9 )XB0PQ9<;N/23<6HC 1:+.B0JIWM68;.9 1N-IGm=L)"/2)Sh67PDCE9�>A\ ¨ GR)~7D68UH9 ¨ � � \

� ���-�98 & � ��6 � % �-,(: ��#B" �Sk-I9§JI9<+:9@3b+:GH;V;.9@6HJ0/Y)IUR1<^kG=P0+.6H/Y)I9@J�de;.GRP 6H)�9b�X7c9<;N/YPQ9@) +.6HC�1:9<+:+./2)0UI^�68;.9Z6HCE=�6@W]1�3bGH;:i

;NBI7D+:9@J^PXWV)IGR/21:9H\�(v)VGRBI;�)ABDPQ9<;N/23<6HC_1:+.B0JIWa=`9�JI9<+:9<;NP /2)I9@JV+.-09�6 oc9@3b+.1�GHd%J0/�oc9<;.9@) +�)IGR/21:9FC29<�H9@C21

Page 5: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz������ �� ybz q�Ns!% � y�NwHr� u{z ��@u{q|w8r � y� �% u� ¨�� .PD6H1:9@J>GR)>+.-I9�6H1.1.BDPQ70+./EGR)�+.-068+TGR)0CEWF1N-IGH+h)0GR/21:9 & de;.GRP +.-I9�1:GRBI;N3b94}{C26H1:9<;&J0/2GXJI9 �¡/21_+.-I9�JIGRP/2)D6H) +)IGR/21.9 3bGR) +:;5/1PDBI+./EGR),+.-I;[email protected];.9@P9@) +�70;.G][email protected]<\�Sk-I9<;.9<deGH;.9H^T=`9?JI9 D)09@J,+.-I9l)IGR/21:9CE9<�H9@C���� � 6H1f+.-I9 1.+.6H)0J068;NJ,J09<�X/268+./2GR)ZGHd`+.-09���s �7 5q|s8r �8q9 u{z q�� �Iu{q{wHr�68;.GRB0)DJM+.-I91./EUR)D6HC��lGHd+.-I94J]ix+.-~1:GRBI;N3b9bi�JI9<+:9@3b+:GH;�7D6H/E;�[email protected];.9@PQ9@)A+k�H9@3b+:GH;� \�Sk-I9�� ��� [email protected];.9@PQ9@)A+J068+.6/Y)�B0)0/E+.1�GHdTJ�*$/21�G=P0+.6H/Y)I9@J�de;.GRP �

� ��� � ¨�� CEGHU & � ����� � � }�>A\ "R�

�M9QdnGRBD)0J~7D;.9<�X/2GRB01.CEW�+.-068+�+.-I9�� ��� GHd GRB0;f9b�X7c9<;N/2P9@) +.6HCh1:9<+vi�BI7M=�6H1�=L/E+.-0/Y) ¨ "aJ�*+:G � "¦J�* }{1:9<9���-D6870+:9<; 5A�5\ g /E�H9@)�+.-068+a;N6H)IUH9§GHd�� ��� =%9MJI9<+:9<;5P/2)I9@J +.-I9Z)IGR/21:9ZCE9<�H9@C�GH;1:+.6H)0JD68;NJZJI9<�X/Y68+./EGR)�� � � dn;.GRP��%�AB068+./2GR)#>A\ "X\��]BIPD1.9@�ABI9@)A+.CEWH^�6 g 6HB01.1N/26H)ZJ0/21:+:;N/>PDBI+:9@JV;56H)0JIGRP)XB0P<Pc9<;%=`6H1�3<6HC23<BDC268+:9@J � � ;[email protected]/. � "cB01N/2)IU4+.-0/Y1%1:+.6H)DJ068;NJlJI9<�X/Y68+./EGR)���� � \ ' )I9<=')IGR/21:9bi�3bGH;.;5BI70+:9@[email protected];.9@PQ9@)A+%�86HC2BI9�=`6H1`G=P0+.6H/Y)I9@JoPXW 6HJ0JD/2)IUF+.-D/21 ;56H)0JIGRPO)AB0P|Pc9<; +:Gj+.-I9�[email protected];N9@PQ9@) +`�86HC2BI9��X\

�M9�3<68;.;5/E9@JVGRBI+�+.-I9�)XB0PQ9<;5/23<6HC�1:+.B0J0WlGR)~dnGRB0;L9b�I6HPQ7DCE9@1L=L/E+.-~JD/�op9<;N9@) +�� ��� 70;.9@1:9@)A+/2)M+.-09 1:W]) +.-I9<+./[email protected];N9@PQ9@) +>J068+.6"}{)0G~)IGR/21:9H^�5 "VJ�*�� ��� ^ �!� J�*�� ��� ^¡6H)0J ¨ "~J�*�� ��� �B01./Y)IU?+.-09>+:9@1.+4PQ9@J0/2B0P 6H1�9b�]7DC26H/2)09@J§/Y)��IBIPD1:9@3b+./EGR) >A\ ¨ \ ¨ \ +T/E;N1:+<^�)0Ga)0GR/21:9j=`6H1f6HJDJI9@JZ+:G�+.-I91:W]) +.-09<+./[email protected];N9@PQ9@) +.1@\ �M9 ;.9@3bGR)01:+:;NBD3b+:9@J,+.-I91.3<68+:+:9<;5/2)IUV3bGX9�� 3</E9@)A+.1 376f1:+.68;N+./2)IU�de;.GRP 6H)/2)0/2+./26HC&[email protected]$3 6 !Q+.-068+Q-06HJ"+.-I9�1.6HPQ9lGH70+./23<6HC`7D68;56HPQ9<+:9<;N1j6H1j+.-I9fPD6H3��XUH;.GRB0)0J[PQ9@JD/2B0P�\§Sk-I9;.9@3bGR)01.+:;NB03b+./EGR) =`6H1l7c9<;.deGH;NPQ9@J B01./2)IUK+.-I9�� g PQ9<+.-0GXJ�^kCYPji * + g ��PQ9<+.-IG]J�^L6H)0J�+.-I9 * + g �PQ9<+.-IG]J�\QSk-I9jG=P��:9@3b+./E�H9d{B0)03b+./2GR)01�GHd`6HC2CT+.-0;.9<9PQ9<+.-IG]J01468;.9J09<7D/23b+:9@JM/2)#+T/EURBI;N9 >A\ � }{6 �5\?Sk-I9�86HC2BI9�GHd�+.-I9�G=P��:9@3b+./E�H9fdeBD)03b+./EGR)l/21%JD/21:7DC26mWH9@J?6H1�6>d{B0)03b+./EGR)?GHd�+.-I9f)XB0P|Pp9<;`GHdmPt6H1./23kGH7c9<;N68+./2GR)01<\' PD6H1./23�GH7c9<;N68+./EGR)�/21�9@/E+.-09<;k6jdnGH;.=�68;NJlGH;L6jUH;N6HJD/E9@) +�3<6HC23<BDC268+./EGR)�\!�]/Y)03b9�+.-09f+./2PQ9�GHdh6>deGH;.=�68;NJ3<6HC23<B0CY68+./EGR)$/21�)I9@68;NC2W�+.-I9,1.6HP9K6H1�+.-068+�GHdjGR)I9MUH;N6HJD/E9@) +V3<6HCY3<B0C268+./EGR)�^�+.-I9,67PD1N3</21.1.6[3<6H) Pc9

� C 4F8:2 $ 8�/ <R� / < 204 � 20/ ���#"%$ ��� ��$&$ ��$ 2(' I S 2 I � 20/@8 $ / $6�Y� �YS 2R.0/ SL��� S I .R. �Y$ 2 ��<R< 8 S / � 2 �)$ 1 /32046204 �*$ / <RS . � 2 ��$F�Y<R< 8�BU204 �S 4 � .0, �-S�� .R.0/ � .Q/ $K<R��� / S 8 $+$ I S 208�. $��-, / S���< Z*. 4 �9S 4 � .0, �-S�� .R.0/ � . <�S . ��� 2 �9� 4F8:208 $�<*/10 . �YS 8 �!/ / $;� 20/ 8 $K� .08 S���<R<R�Y< / $� ��<R� . $ /@8 $���< Z C / $�S��6$ 8+/ <R� . ��� . ��<R�Y$ 2 < . ��$+$ 8 ���20 ' I S 2 I � 20/ $ , �-, ��$ 2 <-3 1 � � I < 2 I <R�6< 2 � 20/ < 20/ S����4$ / < 2R.0/ / I 20/ 8 $F< 208S 4 � . �:S 2 � .0/65 �'$ 8�/ <R� Z87H4 �Y$ 204 � � 4F8:208 $ $ I �9/ � . <�� . ��� � .0, �'�AS 8 $ 20/ $ I 8 I <Q� .08 /;�:/ / � /@2 0�$ / < 2R.0/ / I 20/@8 $ < I S 4 �:< 204 �; � I <R< / ��$<$ / < 2R.0/ / I 20/@8 $ / < $F���-$��)$ Z

Page 6: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨H¨�� ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� /2)A+:9<;.70;.9<+:9@J§6H1�+.-I9>9b�X9@3<BI+./2GR)�+./YPQ9FGHd�+.-09�GH70+./YP/E¥@68+./EGR)~70;.G][email protected]<\ +DBI;.+.-I9<;NPGH;.9H^c=%9jJI9 D)I9�+.-I9)XB0P<Pc9<;�GHd&/E+:9<;N68+./2GR)01�6H1k+.-I9�)AB0P|Pc9<;�GHdhJ09<;N/E�868+./E�H943<6HC23<B0C268+./2GR)01<\

'�1L3<6H)^Pc941:9<9@)~/Y) +h/2URBI;.9�>A\ � }{6 �k+.-I94C2Pji * + g �VPQ9<+.-IG]J�;.9@6H35-I9@J~+.-0941:+:GH707D/2)0U3b;N/E+:9bi;N/EGR)Z68de+:9<;�. � PD6H1./Y3�GH7c9<;N68+./2GR)01<^�=L-0/Y3N-Z3bGR)01./21.+:9@JZGHd " 5VdeGH;.=�68;NJM6H)0J � � UH;N6HJ0/29@) +f3<6HC23<B0CY68+./EGR)01} " 5�� � � ��� \#SL-I9 * + g ��PQ9<+.-IG]J�3bGR)A�H9<;.UH9@J 68de+:9<; ¨ > � PD6H1./23�GH7c9<;N68+./EGR)01M} . � � > 5A�5\�Sk-I9 � gPQ9<+.-IG]J"+:GAG��,+.-09?CEGR)IUH9@1.+�+./2P9 +:G§;.9@6H3N-¦+.-I9l1:+:GH707D/2)0U�3b;N/E+:9<;5/EGR)�^h;.9@�ABD/E;N/2)IU+��.�"kPD6H1./Y3GH7c9<;N6 i+./EGR)01l}��� �� � � �5\~Sk-0967PD1:GRC2BI+:9?)AB0P|Pc9<;4GHd�deGH;.=`68;5JM;NB0)01F6H)0J,UH;N6HJD/E9@) +�3<6HC23<B0C268+./EGR)D14J0/�oc9<;.9@J�^JI9<7c9@)0J0/Y)IUZGR)�+.-I9§PQ9<+.-IG]J�B01.9@J�\���1.BD6HC2CEW¦+.-I9�� g PQ9<+.-IG]J P 6HJI9~PQGH;.9�dnGH;N=`68;NJ�;NB0)01?6H)0Jde9<=%9<;fUH;N6HJD/E9@) +f3<6HC23<BDC268+./EGR)01�+.-06H)Z+.-I9� � PQ9<+.-IG]J01<^YPc9@3<6HB01:9>+.-I9�� g PQ9<+.-IG]JMB01:9@JZ6H)§9b�I6H3b+C2/2)09�1:9@68;N35-,}{C2/2)I9bi�P /2)0/2P/2¥@68+./EGR)�^R1:9<9 �]BIPt1:9@3b+./EGR) "X\ � \ ¨ �5\`Sk-09 * + g �lP9<+.-IGXJa6H)0Jl+.-I9fC2PQi * + g �PQ9<+.-IG]J�B01:9@J�6H)�/2)I9b�I6H3b+?CY/2)I9~1:9@68;53N-£} PD6H3��X+:;N6H3/�X/2)0U¦PQ9<+.-0GXJ�^k1.9<9��]B*PD1:9@3b+./EGR) "X\ � \ ¨ �5^L=L-0/Y3N-;.9@�XB0/E;.9@J�[email protected];.=�68;NJ¤;NBD)01QdeGH; 9@6H3N-�1:9@68;N35- JD/E;.9@3b+./EGR)�\'Sk-I9 t)06HC��86HC2BI9 �� GHd�+.-I9�G=P��:9@3b+./E�H9d{B0)03b+./EGR)¦=�6H1QJ0/�oc9<;.9@) +jdeGH;6HC2C`+.-I;.9<9�PQ9<+.-IG]J01<\¦Sk-I9 * + g ��P9<+.-IGXJ[-06HJ[+.-09a1NP6HC2CE9@1:+>�86HC2BI9CEGHU & � }��� � � : " � � � ^D=L-I9<;N9@6H1�+.-I9 � g PQ9<+.-IG]JV-06HJ�+.-I94CY68;.UH9@1:+k�86HC2BI94CEGHU & � }��� � � : 5 � 5 � \

Sk-I9%;[email protected]+./Y)IUk/2P68UH9`;.9@3bGR)01:+:;5B03b+./EGR)01_GHd 376_=L/E+.-IGRBI+h)IGR/21:9`68;.9%JD/21:7DC26mWH9@J�/Y)'+T/EURBI;.9 >A\��X\Sk-I9§/2)A+:9<;.� 6HCJPc9<+�=`9<9@)�6HJ�:6H3b9@)A+l/Y1:GRC2/2)I9@1 /21 3$# � ¨ 3<P�� & \�SL-I9�/2P 68UH9�6H3<3<BI;N6H3bW /21?-D/EUR-I9@1:+} % 4 /214-0/2UR-I9@1:+46H)0J %7/ /21f1.P6HCYCE9@1:+5��deGH;4+.-I9 /2P 68UH9G=P0+.6H/2)I9@J PAW§+.-I9 * + g �,PQ9<+.-IG]J�} %�������4 %���� � ������4 %�� �4 6H)DJ % ������/ % ��� � ������/ %�� �/ �5^D1.9<9F6HC21:G Sh67PDCE9�>A\ ¨ \

'�)0GH+.-I9<;�PQ9<+.-0GXJKGHd�3bGRP7D68;N/21:GR)K/214+:G§CEGAG��M68+�+.-I9;.9@3bGR)01.+:;NB03b+./EGR)K;[email protected]+.1F68dn+:9<;>+.-I91.6HPQ9�)XB0P|Pp9<;hGHd6Pt6H1./23%GH7p9<;568+./EGR)01<^8=L-0/Y3N->/2PQ7DC2/29@1�+.-I9�1.6HPQ9�3bGRPQ7tBI+.68+./EGR)06HCX+./2PQ9H\[email protected]%;.9@1NB0CE+.168;.9,1.-0Gm=L)$/2)1+T/EURBI;N9 >A\65I\ (v)'+.-0/21�0URB0;.9Z=%9M70;N9@1:9@) +�+.-09Z/YP68UH9@1�G=P0+.6H/2)09@J$68dn+:9<; . � PD6H1./23GH7c9<;N68+./EGR)014dnGH;�9@6H3N-¦PQ9<+.-IG]J�\ Sk-0/Y1f)AB0P|Pc9<;4=�6H1F1:9@CE9@3b+:9@J Pc9@3<6HB01:9 /E+�/21�+.-I9?)XB0P|Pc9<;fGHd�1.+:9<7D1)I9<9@JI9@J§deGH;�+.-I9jde6H1:+:9@1.+�P9<+.-IGXJ�}{C2PQi * + g �0�L+:G�1.68+./21:deWV+.-I9j1:+:GH707D/Y)IUl3b;5/E+:9<;N/EGR)�\�Sk-XB01<^p+.-I9QC2Pji* + g �V/2P68UH9f=�6H1�G=P0+.6H/2)I9@J�68de+:9<; � � /2+:9<;N68+./EGR)014} " 5�� � � �5^p+.-I9#* + g ��/2P68UH9F68de+:9<; 5��Q/E+:9<;568+./EGR)01��� .08 � $ 8 1 8 $ 1 � 1 / �@� 1 .0/32 � 204 � $ I �9/ � .#8�B BT8:. 1 � . $ ��$+$ ,�. � $ / ��$ 2 S����@S I � � 20/ 8 $F< 1 /3204F/ $��F� . ��$ 204 �Y<R��< � B 8�. 1 � . $SL�:� S I � � 20/@8 $�<"! ,:. � $ / ��$ 2 SL�:� S I � � 20/@8 $�<$# Z

Page 7: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨H¨H¨

0 50 100 150 200 250 300 350 400−5.5

−5

−4.5

−4

−3.5

−3

−2.5

−2

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� ��#�� 8 $ 8+/ <R� Z0 100 200 300 400 500

−4.5

−4

−3.5

−3

−2.5

−2

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� /#�� � $ O C��DG Z

0 50 100 150 200 250 300 350 400−2.1

−2.05

−2

−1.95

−1.9

−1.85

−1.8

−1.75

−1.7

−1.65

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� S # � * $ O C��DG Z0 50 100 150 200 250 300

−1.6

−1.55

−1.5

−1.45

−1.4

−1.35

−1.3

−1.25

−1.2

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� $ # 7 � $ O C��DG Z+T/EURBI;.9 >A\ �$��� P��:9@3b+./E�H9�d{B0)03b+./EGR)01 dnGH;�J0/Eop9<;.9@)A+�1./EUR)06HC�ix+:G8i�)0GR/21:9L;568+./EGR1`GHd�+.-I9f1:W]) +.-I9<+./Y3�PQ9@6H1NBI;.9biPQ9@)A+LJ068+.6]\

Page 8: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨H¨ � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

� ��#�� ; ��� 204�8 $ 3 � B 2 � .> � � /F��< / S 8 � � . � 20/ 8 $F< Z� / #D� � " O � ; CK��� 204F8 $ 3� B 2 � .�� � /;��< / S 8 � � . � "20/@8 $�< Z

7��

� �� � ��� �

� S # O � ; C ��� 204�8 $ 3 � B�2 � . 7�� �/;�:< / S 8 � � . � 20/ 8 $F< Z

+T/EURBI;.9 >A\�� � +T/2)06HC¡/YP68UH9�;N9@3bGR)01:+:;NB03b+./2GR)01LGHd�376@\ � Gl)IGR/Y1:94=�6H1�7D;.9@1:9@)A+�/2)~+.-I9>1.WX)A+.-I9<+./23�PQ9@6 i1.BI;N9@PQ9@) +kJD68+.6]\���/21:+.6H)03b9<Pp9<+ =%9<9@)�6HJ �.6H3b9@) +L/Y1:GRC2/2)I9@1�/21 ¨ 3<P�� & \

� � #�� ; ��� 204F8 $ 3W� B 2 � .� � /F��< / S 8 � � . � 20/ 8 $F< � �/32 � . � 20/@8 $�<$# Z

� /#%�@� " O � ; CK��� 204F8 $ 3� B 2 � . � � /;�:< / S 8 � � . �:"20/ 8 $F< � > X-/@2 � . � 20/@8 $�<$# Z

� �

� ���� �

� S # O � ; C'��� 204F8 $ 3�� B�2 � . � � /;�:"< / S 8 � � . � 20/@8 $�< � ��� /32 � . � 20/@8 $F<$# Z

+T/EURBI;.9 >A\65 � (*P68UH9�;.9@3bGR)01:+:;5B03b+./EGR)01LGHd�376L68de+:9<; . � PD6H1./Y3fGH7c9<;N68+./EGR)01<\ � G?)IGR/Y1:94=�6H1�7D;.9@1:9@)A+L/2)+.-I9F1.WX)A+.-I9<+./23fPQ9@6H1NBI;.9@PQ9@)A+LJ068+.6]\���/21.+.6H)03b9,Pc9<+�=`9<9@)~6HJ �.6H3b9@)A+�/21:GRCY/2)I9@1�/21 ¨ 3<P�� & \

Page 9: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨H¨ �}�5��� 5��R�5^c6H)0J�+.-I9�� g /2P68UH9F68de+:9<; >Q/E+:9<;N68+./EGR)01�} � "� >H�5\

�M9KJ0/2J�+.-I9,1N6HPQ9K1:+.B0J0W�deGH;~6�1:9@3bGR)0J$9b�I6HPQ7DC29H^�=�-I9<;.9Z=%9"6HJ0JI9@J$C2/E+:+.C29Z)0GR/21:9Z+:G+.-I9j1:W]) +.-I9<+./Y3>[email protected];.9@PQ9@)A+�J068+.6l;[email protected]+./Y)IU /2)§6 � ��� GHd)5 "?J *�\cSk-I9>G=P��:9@3b+./E�H9jdeBD)03b+./EGR)01�68;.91.-IG =L)Q/2) +T/EURBI;.9 >A\ � } Pp�5\�SL-I9�C2Pji * + g �jP9<+.-IGXJQ)09<9@JI9@J . ¨ PD6H1./Y3%GH7c9<;N68+./2GR)01k} "�"� ��R�5^]6H)0Jj+.-I9* + g �>PQ9<+.-0GXJ�+:GAG�� . � PD6H1./23 GH7p9<;568+./EGR)01�} " 5�� 5 5A�5\�Sk-I9 � g PQ9<+.-IG]J�+:GAG���5 .�"JPt6H1./23%GH7p9<;568+./EGR)01}�5 " 5�� 5 ¨ �fdnGH;F3bGRP7DCE9<+./EGR)�\jSk-I9 D)D6HC_�86HC2BI9@1f68de+:9<;4+:9<;NP /2)068+./EGR)M68;.9C2GHU & � }��� � � : 5 � 5 � deGH;4+.-I9* + g �V6H)0JVC2Pji * + g ��PQ9<+.-IG]J�^06H)0J~CEGHU & � }��� � � : 5 � � � dnGH;k+.-09�� g PQ9<+.-0GXJ�\

Sk-I9 � ��� GHd�+.-I9?+.-0/E;NJM9b�I6HPQ7DC29 =�6H1 �!� J�*�^¡=L-D/23N-"/214+ WA7D/Y3<6HC2CEW§9@)03bGRB0)A+:9<;.9@J¦=L-I9@)7c9<;.deGH;NP/2)IUM9b�]7c9<;N/2PQ9@)A+.1GR)�+./21N1.BI9"}{1:9<9 ��-0687D+:9<; 5A�5\ Sk-I9~G=P��v9@3b+./E�H9§d{B0)03b+./EGR)01 GHdF6HC2CL+.-I;.9<9GH70+./2P /E¥@68+./EGR)§+:9@3N-0)D/2�AB09@1�68;N9Q70;.9@1:9@)A+:9@JZ/2) +h/2URBI;.9 >A\ � }{3m�5^h6H)0J§+.-I9Q/2P 68UH9>;N9@3bGR)01:+:;NB03b+./2GR)01f68;.91.-IG =L)�/Y) +T/EURBI;.9 >A\ "X\�Sk-I9§/2P68UH9�6H3<3<B0;N6H3bW�/21?-0/EUR-I9@1:+ dnGH;iPpGH+.- +.-I9§C2Pji * + g ��6H)0J * + g �PQ9<+.-IG]J$}{1:9<9VSh67PDCE9 >A\ ¨ �5\"Sk-09�t)06HC ;N9@3bGR)01:+:;NB03b+./2GR)01j=%9<;N9lG=PD+.6H/2)I9@JbPAW¦B01./2)0U�+.-I9�C2PQi * + g �PQ9<+.-IG]J,68de+:9<; � �^PD6H1./23jGH7c9<;N68+./EGR)D1 } ¨ "� ¨H¨ �F6H)0J`PXW§B01N/2)IUa+.-I9 * + g �KPQ9<+.-IG]J,68de+:9<; � �^PD6H1./23GH7c9<;N68+./EGR)01Q} ¨ � � ¨H¨ �5\>Sk-I9 � g PQ9<+.-IG]J§+:GAG�� ���"fPD6H1./23�GH7c9<;N68+./EGR)01Q}�� 5.�� � � ��dnGH;f3bGRPQ7DC29<+./EGR)�\Sk-I9 D)06HC_�86HC2BI9>GHd�+.-I9>G=P��v9@3b+./2�H9QdeB0)D3b+./EGR)~=�6H1�CEGHU & � }��� � � : ��� � >?deGH;�+.-I9 * + g �§PQ9<+.-IG]JZ6H)0JC2Pji * + g �'PQ9<+.-IG]J�^�6H)0J$CEGHU & � }��� � � : ��� ��� deGH;V+.-I9 � g P9<+.-IGXJ�\O(v) +T/EURBI;.9 >A\ �[=`9,1.-IG =;.9@3bGR)01.+:;NB03b+:9@J�/2P68UH9@1�GHdh6HC2Cp+.-I;.9<94PQ9<+.-0GXJ01`deGH;�+.-I9f1.6HPQ9f)XB0P<Pc9<;�GHdmPt6H1./23�GH7p9<;568+./EGR)01<\&(v)l+.-0/213<6H1:9H^T+.-I9�* + g �,P9<+.-IGXJK=`6H1�+.-I9?de6H1:+:9@1.+�PQ9<+.-IG]JK1N68+./21:deWX/2)0U�+.-I9?1:+:GH7D7D/2)IUV3b;N/2+:9<;N/EGR)M=L/2+.- � �PD6H1./Y3�GH7p9<;568+./EGR)01 6H)DJ ¨H¨ /E+:9<;568+./EGR)01<\ � �XB0/E�86HCE9@)A+.CEWH^R+.-I9�C2Pji * + g �PQ9<+.-IG]J )I9<9@JI9@J ¨�� /E+:9<;568+./EGR)01deGH;?+.-I9§1.6HPQ9Z6HPQGRB0)A+?GHd{Pt6H1./23VGH7c9<;N68+./2GR)01<\ Sk-I9�� g PQ9<+.-IG]J 3bGRPQ7tCE9<+:9@J�GR)DCEW ¨ /E+:9<;568+./EGR)�\'�143<6H)`Pc9Q3<CE9@68;NCEW§1:9<9@)�^�+.-I9/YP68UH96H3<3<BI;N6H3bWM/21f-0/2UR-I9@1:+�dnGH;F+.-I9Q/2P68UH9@1fG=P0+.6H/Y)I9@J[PAW§+.-I9 �PQ9<+.-IG]J01F}{1.9<9FS_67PtCE9�>A\ ¨ �5\

(*)~6QdnGRB0;.+.-�9b�I6HPQ7DCE94=`9�J09@3b;.9@6H1:9@JV+.-09 � ��� GHdT+.-I9F1.WX)A+.-I9<+./[email protected];.9@PQ9@)A+LJ068+.6 +:G¨ "fJ�*�\RSk-09 * + g �QPQ9<+.-0GXJQ)I9<9@J09@J � >aPD6H1./Y3%GH7c9<;N68+./2GR)01L} ¨ "� ¨ � �5\ SL-I9�C2Pji * + g �PQ9<+.-IG]Jj+:GAG��� � PD6H1N/23fGH7c9<;N68+./EGR)01�} ¨ � � ¨�� �5\`SL-I9�� g P9<+.-IGXJ~JI9@P6H)0JI9@JV+.-I9FPQGR1:+�3bGRPQ7DBI+.68+./EGR)D6HC�+./2PQ9fdeGH;

Page 10: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨H¨ 5 ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

� � #�� ; ��� 204F8 $ 3 � B�2 � .> � � /F��< / S 8 � � . � 20/@8 $�< Z

� / #%�@� " O � ; CK��� 204F8 $ 3� B 2 � . � ��/;�:< / S 8 � � . � "20/@8 $F< Z

� �

� �� �� �

� S # O � ; C'��� 204F8 $ 3�� B�2 � . ��> /;� "< / S 8 � � . � 20/@8 $�< Z

+T/EURBI;.9 >A\ " � +h/Y)06HCD/2P 68UH9k;.9@3bGR)01:+:;5B03b+./EGR)01%GHd 376<\&Sk-I9 � ��� GHd�+.-I9L1.WX)A+.-I9<+./23�[email protected];.9@P9@) +`J068+.6=�6H1 �!� J�*�\ ��/21:+.6H)D3b9,Pc9<+�=`9<9@)~6HJ �.6H3b9@) +�/21:GRC2/Y)I9@1�/21 ¨ 3<P�� & \

� � #�� ; ��� 204F8 $ 3 � B�2 � .��> /;�:< / S 8 � � . � 20/@8 $�< � 7/@2 � . � 20/@8 $ # Z

� / #%�@� " O � ; CK��� 204F8 $ 3� B 2 � . ��> /;�:< / S 8 � � . � "20/@8 $F< � 7 * /32 � . � 20/@8 $F<$# Z

� �

� �� �� �

� S # O � ; C'��� 204F8 $ 3�� B�2 � . ��> /;� "< / S 8 � � . � 20/@8 $�< � 7�7 /32 � . � 20/@8 $�<$# Z

+T/EURBI;.9 >A\ � � (vP68UH9k;N9@3bGR)01:+:;NB03b+./2GR)01&GHd 376�68de+:9<; � �,PD6H1./23�GH7c9<;N68+./EGR)D1<\hSL-I9�� ��� GHdc+.-I9L1:W])A+.-I9<+./[email protected];.9@PQ9@)A+LJ068+.6Q=�6H1 �!� J *�\ ��/21.+.6H)03b9,Pc9<+�=`9<9@)~6HJ �.6H3b9@)A+�/21:GRCY/2)I9@1�/21 ¨ 3<P�� & \

Page 11: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨H¨ "

3bGRPQ7DC29<+./EGR)�\&Sk-I9�GH70+./2P/2¥@68+./EGR) 7D;.GX3b9@1N1%=�6H1�+:9<;NP/Y)068+:9@J?68de+:9<; � . >|PD6H1./Y3kGH7c9<;N68+./EGR)01f} � �]¨ � ¨ �R�5\Sk-I9�G=P��:9@3b+./E�H9jdeB0)D3b+./EGR)01L68;N9>1.-0Gm=L)§/2) +h/2URBI;.9 >A\ � }{Jp�k=�/E+.-V+.-I9 D)06HC_�86HC2BI9@1�CEGHU & � }��� � � : ¨�� " �deGH;k+.-I9 * + g �V6H)0JVC2PQi * + g ��PQ9<+.-0GXJ�6H)0J~CEGHU & � }��� � � : ¨�� " 5?dnGH;k+.-09 � g PQ9<+.-0GXJ�\� ���-��� & � ��6 � % �-,A��# � � 3:��)*% &E)�#(%'#(6 >�� ���"$" ��"

�M9~6HC21:G,1.+.B0J0/E9@J[+.-I9�/2)�DBI9@)D3b9?GHdfJ0/�oc9<;.9@)A+-IGRPQGHUH9@)I9<GRBD1 /2)0/2+./26HC [email protected]:9@1 376 ! \ �M9-06m�H9V3N-IGR1:9@)¦+.-I;N9<9aJD/�op9<;N9@) +>9b�]6HP7DCE9@1�GHd�376�!Q=L/E+.-¦6 �!� � ^)� � � 6H)0J " � � -0/EUR-I9<;j1.3<68+:+:9<;N/Y)IU3bGX9�� 3</E9@)A+ +.-06H)�+.-I9~GH;N/2UR/2)06HC�PQ9@J0/YB0P�\ SL-I9VG=P��:9@3b+./E�H9~d{B0)03b+./2GR)01QGHd46HC2C�+.-0;.9<9~9b�I6HPQ7DCE9@1?68;.91.-IG =L)V/2) +T/EURB0;.9�>A\ >A\

+T/EURBI;.9 >A\ >]}{6 ��1.-IG =L1`+.-I9�;[email protected]+.1`GHd�+.-I9 0;51:+ 9b�I6HPQ7DCE9�=L-I9<;N9�6 �!� � -0/EUR-I9<;�1.3<68+:+:9<;N/Y)IU3bGX9�� 3</E9@)A+?deGH;?+.-09�/2)0/2+./26HC�[email protected]?=�6H1l35-IGR1:9@)�\�Sk-I9 � PQ9<+.-IG]J01=`9<;.9§de6H1:+:9<;a+.-06H) +.-I9�� gPQ9<+.-IG]J�^&6H)0J¦6HC21:G§;.9@6H3N-09@J¦6§1.P6HCYCE9<;��86HC2BI9 �� GHdk+.-09?G=P��:9@3b+./E�H9ldeBD)03b+./EGR)"=L-I9@),+.-09l1:+:GH7D7D/2)IU3b;N/E+:9<;5/EGR)M=�6H1>1N68+./2109@J�\aSk-I9�* + g �KPQ9<+.-IG]JK)I9<9@JI9@J ¨ 5 � PD6H1./23QGH7c9<;N68+./2GR)01?} � >��� ¨ ��6H)0JK+.-I9C2Pji * + g �¤PQ9<+.-0GXJ�3bGRPQ7DCE9<+:9@J�68de+:9<; ¨ " � PD6H1./23~GH7c9<;N68+./EGR)01§} � .��� ¨ � =L/E+.-�C2GHU & � }��� � � : " �2¨ �6H)0JZCEGHU & � }��� ��� : " � � "X^_;.9@1:7c9@3b+./E�H9@CEWH\FSL-I9�� g PQ9<+.-IG]J§+:GAG��§+.-I9QCEGR)IUH9@1:+f;N9@�AB0/2;N/2)IU ��. � PD6H1./23GH7c9<;N68+./EGR)01�}����� � � ��=�/E+.-�CEGHU & � }��� � � : 5 � 5I\

Sk-I91:9@3bGR)DJM9b�]6HP7DCE9Q=L/E+.-M6 � � � -0/EUR-09<;F1.3<68+:+:9<;N/2)0U~3bGA9��?3</E9@) +l}{1:9<9�+T/EURBI;.9 >A\ >]} Pc�:�1.-IG =L1�Pt6H1./23<6HC2CEWj6F1N/2P/2C268;&;[email protected]+�6H1%+.-I9 D;N1:+&9b�I6HPQ7DCE9H\&Sk-I9�C2Pji * + g � PQ9<+.-IG]J )I9<9@J09@J � 5nPD6H1./23GH7c9<;N68+./EGR)01�} " ¨ � � �R�%=L/2+.-?CEGHU & � }��� � � : 5 � 5 � +:Gj3bGR)A�H9<;.UH9H\`Sk-I9 * + g �lPQ9<+.-IG]J?3bGR)A�H9<;.UH9@J�68de+:9<;�]¨ �<PD6H1./23�GH7c9<;N68+./2GR)01�} ¨ � �� � >H� =L/2+.-+.-I9�1.P6HC2CE9@1.+&� 6HC2B09LGHd�CEGHU & � }��� � � : " � � "F3bGRPQ7t68;.9@J+:G>+.-I9GH+.-I9<;�+:9@3N-0)0/Y�ABI9@1@\?Sk-I9 � g PQ9<+.-0GXJM+:GXG��M+.-I9 C2GR)IUH9@1:+4+./2P9+:G�1.68+./Y1:dnW§+.-I9 1.+:GH7"3b;N/E+:9<;5/EGR)�\ (*+D)0/Y1.-I9@J>68dn+:9<; 5 �]¨ Pt6H1./23`GH7c9<;N68+./EGR)01�}�� � .� � � �&=L/E+.-jCEGHU & � }��� � � : 5 � � "X\�SL-I9 D)06HCX;.9@3bGR)01:+:;5B03b+:9@J/2P68UH9@1L68;.941.-IG =L)V/2) +T/EURBI;.9�>A\ � \ '�JDJ0/E+./EGR)06HCYCEWH^ =`9F6HC21:GQ3bGRPQ7t68;.9@JV6HC2Cc+.-I;N9<94PQ9<+.-IG]J01k68de+:9<; � 5PD6H1./Y3LGH7c9<;N68+./EGR)D1<^]+.-I9�7pGR/Y) +�68+�=L-0/235-l+.-I9fC2Pji * + g �lPQ9<+.-0GXJa=�6H1�+.-I9 0;N1:+`+:G1.68+./21.dnW+.-0941:+:GH7Ii7D/2)0U�3b;N/E+:9<;5/EGR)�\&Sk-I9�C2Pji * + g �?PQ9<+.-0GXJlW]/E9@C2JI9@Jl68dn+:9<; � �>/E+:9<;568+./EGR)01`+.-I9�/2P68UH9f/2) +h/2URBI;.9 >A\ .I} Pp�

Page 12: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨H¨ � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

0 50 100 150 200 250 300 350 400−5.5

−5

−4.5

−4

−3.5

−3

−2.5

−2

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� ��#-& $ /320/ �:� , I �Y<R<�� ��� 1 ��< � *�� 4�/ ,�4 � . 204 ��$ 204 �/F��S�� ,�.08 I $&$ <RSL� 2R2 � .0/ $ ,N8�B�204 � 8�.0/@,+/ $F��� ���)$ / I � Z

0 100 200 300 400 500−5.5

−5

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� / #9& $ /320/ ��� , I ��<R<�� ��� 1 �:< > *� 4F/@,+4 � . 204 ��$ 204 �/F��S�� ,�.08 I $&$ <RSL� 2R2 � .0/ $ ,�8�B 204 � 8�.0/@,+/ $;�:�U���)$ / I � Z

0 100 200 300 400 500−6

−5

−4

−3

−2

−1

0

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

� S #%& $ /320/ ��� , I ��<R<� ��� 1 �:< ��*�� 4F/@,+4 � .Q204 �:$ 204 �/;�:S�� ,:.08 I $+$ <RS�� 2R2 � .0/ $ ,-8�B 204 � 8:.0/ ,�/ $;��� ���)$ / I � Z

+T/EURBI;.9�>A\ > � � P��v9@3b+./2�H94deBD)03b+./EGR)01�deGH;LJ0/�oc9<;.9@)A+k/2)0/E+./[email protected] 376�!m\

Page 13: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨H¨ >

� � #�� ; ��� 204F8 $ 3 � B�2 � .� ��7 /F��< / S 8 � � . � 20/@8 $�< Z

� / #%�@� " O � ; CK��� 204F8 $ 3� B 2 � .HX � /;�:< / S 8 � � . � "20/@8 $F< Z

� �

� �� �� �

� S # O � ; C ��� 204�8 $ 3A� B�2 � . ��7L>/F��< / S 8 � � . � 20/@8 $F< Z

+T/EURBI;.9 >A\ �$� +T/2)06HC&/2P68UH9 ;.9@3bGR)01:+:;NBD3b+./EGR)01fGHd�3 6 \Q(v)0/E+./[email protected] 3 6 !�=�6H1 � � � -0/EUR-I9<;4+.-D6H)M+.-I9PD6H3/�AUH;.GRBD)0J�1N3<68+:+:9<;N/2)IU�GHd0+.-I9%GH;N/EUR/2)D6HC PQ9@J0/YB0P�\ ��/21.+.6H)03b9 Pc9<+ =%9<9@)j6HJ �.6H3b9@) +&/21.GRC2/2)I9@1�/Y1 ¨ 3<P � & \

� � # � ; ��� 204�8 $ 3W� B 2 � .X � /F��< / S 8 � � . � 20/@8 $F< � �/32 � . � 20/@8 $F<$#

� /#D�@� " O � ; CK��� 204�8 $ 3� B�2 � . X � /F��< / S 8 � � . �:"20/@8 $�< � >�> /32 � . � 20/@8 $�<$#

7��

� �� � ��� �

� S # O � ; C ��� 204�8 $ 3�� B�2 � .%X � /F�:"< / S 8 � � . � 20/ 8 $F< � � *N/32 � . � 20/ 8 $F<$#

+T/EURBI;.9 >A\ . � (vP68UH9V;.9@3bGR)D1:+:;NB03b+./EGR)D1jGHd�376Q68de+:9<; � 5 PD6H1N/23lGH7p9<;568+./EGR)01<\¦Sk-I9�/2)0/E+./Y6HC URBI9@1N1 376 !=�6H1 � � � -D/EUR-I9<;k+.-06H)V+.-I9,PD6H3/�AUH;.GRBD)0J~1.3<68+:+:9<;5/2)IUGHdT+.-I94GH;5/EUR/2)06HC�PQ9@JD/2B0P�\ ��/21:+.6H)D3b9,Pc9<+�=`9<9@)6HJ �.6H3b9@) +�/21:GRC2/Y)I9@1�/21 ¨ 3<P�� & \

Page 14: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨H¨ � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� 6H)0JK+.-I9 * + g �"PQ9<+.-IG]J,)I9<9@J09@J 5 � /E+:9<;N68+./EGR)01�6H)0JMW]/E9@C2JI9@J,+.-I9 /2P68UH9l1:9<9@)¦/2) +T/EURBI;.9 >A\ .I}{3m�5\Sk-I9 � g P9<+.-IGXJK+:GAG�� �~/E+:9<;N68+./EGR)D1F6H1>1:9<9@)"/Y) +T/EURBI;.9 >A\ .I}{6 �5\§Sk-I9 * + g �KP9<+.-IGXJ"6H3N-0/29<�H9@J;.9@3bGR)01.+:;NB03b+:9@J/2P 68UH9@1�=L/E+.-j+.-09k-0/EUR-I9@1:+�/YP68UH9k6H3<3<BI;N6H3bWV} % 4�=�6H1�-0/EUR-I9@1.+�6H)0J %0/ =�6H1�1.P6HCYCE9@1:+5�5^1:9<9F6HCY1:GS_67PtCE9�>A\ ¨ \

0 20 40 60 80 100 120−6

−5

−4

−3

−2

−1

0

1

2

3

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

BFGS method BFGS method (pos. def. Hessian)

+T/EURBI;.9 >A\ ¨���� � P��:9@3b+./E�H9Fd{B0)03b+./2GR)01kB01./Y)IU+.-I9(* + g ��PQ9<+.-IG]JV=L/E+.-�� =L/E+.-IGRBI+k6 7cGR1./E+./E�H9FJ09 D)0/E+:9/2)A�H9<;N1:9��L9@1N1./26H)�\ '�)l/Y)0/E+./[email protected] " � � -D/EUR-I9<;`+.-06H) +.-09ZPD6H3/�AUH;NGRB0)0Ja1.3<68+:+:9<;N/2)0U>GHd¡+.-I9�GH;5/EUR/2)06HCPQ9@J0/YB0P CE9@J�+:G 6���[email protected]./Y6H)�+.-068+k=�6H1k)IGH+k7cGR1./2+./E�H9fJI9 D)0/E+:9H\

Sk-I9�C26H1:+&9b�I6HPQ7DC29kB01:9@J6f1:+.68;N+./2)IUf7cGR/2)A+�376 ! =L/E+.-Q6'" � � -0/EUR-I9<;�1.3<68+:+:9<;5/2)IUF3bGX9�� 3</E9@)A+}{1:9<9#+T/EURBI;.9 >A\ >]}{3m�:�5\�SL-I9§CYPji * + g ��PQ9<+.-IG]J')I9<9@JI9@J ¨ >" PD6H1./23�GH7c9<;N68+./EGR)01M} . � � >�>H�5\�Sk-I9* + g �KPQ9<+.-IG]J D)0/Y1.-I9@JM68de+:9<; �]¨ >^PD6H1./23jGH7c9<;N68+./EGR)D1?} ¨H¨ � � .�.R�5\VSk-09�� g +:9@35-0)0/2�XBI9+:GXG��M+.-I9CEGR)IUH9@1.+F+./2PQ9?+:G�;N9@6H3N-¦+.-I9?1.+:GH7¦3b;N/2+:9<;N/EGR)�\�(*+ D)D/21.-I9@J,68de+:9<;-5 ¨ � Pt6H1./23GH7c9<;N68+./2GR)01?}�� �]¨ � � ¨ �5\Sk-I9�D)06HC`�86HC2BI9@1>GHdL+.-09lG=P��v9@3b+./E�H9ad{B0)03b+./EGR)¦=`9<;.9�CEGHU & � }��� � � : " �2¨ .§deGH;Q+.-I9$* + g �¦PQ9<+.-IG]J�^CEGHU & � }��� ��� : 5 � .�.,dnGH;+.-09~C2Pji * + g ��PQ9<+.-IG]J�^`6H)DJ�CEGHU & � }��� � � : 5 �2¨ �ZdeGH;+.-I9 � g PQ9<+.-IG]J�\Sk-0/Y1�;.9@3bGR)01.+:;NB03b+./EGR)?9b�]6HP7DCE9�/Y1 GHd�7t68;.+./23<B0C268;%/2) +:9<;N9@1:+%deGH;`+.-I9� � PQ9<+.-IG]J01<^?Pp9@3<6HBD1:9ZPcGH+.-?+.-I9* + g �aP9<+.-IGXJ�6H)DJa+.-I94C2Pji * + g ��PQ9<+.-IG]J�6HBI+:GRP68+./23<6HC2C2W ;.9<7DCY6H3b9@Ja+.-I94687070;.Gm�]/YP68+:9@J�/2)A�H9<;N1:9��[email protected]./26H)¤P 68+:;N/��"=�/E+.-[+.-I9V/2JI9@)A+./E+ W¦P68+:;5/��¦68de+:9<; +.-I9 D;N1:+/E+:9<;N68+./2GR)[+:G,70;.9<�H9@)A+ 6Z70;.9@P 68+.BI;.93bGR)A�H9<;.UH9@)03b9H\

Sk-I9Q�XB06HJI;N68+./23jPQG]JI9@C|^�6H1fUR/2�H9@)`PAW � �XB068+./EGR) "X\ ¨ .X^_=`6H14)0GH+46aUHGAG]JM687070;.Gm�]/YP68+./EGR)

Page 15: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨H¨ .

GHdF+.-09§G=P��v9@3b+./E�H9Md{B0)03b+./2GR) 68+�+.-0/Y1?/2)D/E+./26HC�[email protected]<\�SL-I9§/Y) �H9<;N1.9 ��[email protected]./Y6H)����,68+a+.-I9M1:+.68;N+./2)IU7cGR/2)A+�����!?=`6H1)0GH+Q7pGR1N/E+./E�H9�JI9 D)0/2+:9a6H)DJ[+.-I9V3<BI;.�868+.BI;.9V3bGR)0JD/E+./EGR) }{1:9<9 �%�ABD68+./EGR) "X\ � � �j=�6H1)IGH+f1.68+./21 09@J�\fSk-I9>GH70+./2P/2¥@68+./EGR)§70;.G][email protected]�GHd�+.-I9 * + g �ZPQ9<+.-0GXJ§+:9<;NP/Y)068+:9@JZ68dn+:9<;43bGRPQ7tCE9<+./2)IUGR)0CEW +.-I9 0;N1:+�/E+:9<;568+./EGR),}{1:9<9 +T/EURBI;.9'>A\ ¨�� �5\`Sk-I9 D)06HCp�86HC2BI9�GHd¡+.-I9fG=P��v9@3b+./E�H9fd{B0)03b+./2GR)?=�6H1�GR)0C2WCEGHU & � }��� ��� : ¨�� �I¨ \~Sk-I9<;N9<dnGH;.9H^h+.-I9l687070;.Gm�]/2P 68+:9@J"/2)A�H9<;N1:9 �[email protected]/26H),=�6H1F;N9<7DC26H3b9@JK68+>+.-I9�0;N1:+/E+:9<;N68+./2GR)V1:+:9<7V=L/2+.-a+.-I9F/2JI9@)A+./E+ WlP68+:;5/���� ���§6H1�9b�X7tC26H/2)I9@J�/2) �IBIPD1:9@3b+./EGR) "X\ � \ "X\

�� ��� �� &������������� (:!��"$#�%!��&�' &�&�"(�)"���* � ��%+#,#

(*) 70;N6H3b+./23b9H^]=`9�+ WA7t/23<6HC2CEWj9@)03bGRB0)A+:9<;�+.-I9�1./E+.B068+./EGR)�^ =L-I9<;N9L+.-I9�[email protected];N9@PQ9@) +`J068+.6j68;.93bGH;.;NB070+:9@J^PXWV)IGR/21:9>6H)0JV+.-09>/2)D/E+./[email protected]�/21�)IGH+�3<C2GR1:9F+:Gl+.-I9�1.GRC2BI+./EGR)�^D9H\ Ua/2+LJIGX9@1�)IGH+�3<CEGR1:9@CEWP68+.35-a+.-I9ZPt6H3��XUH;.GRB0)0JaPQ9@J0/YB0P�\*�M94JI9@PQGR)01:+:;568+:9�+.-I9�7c9<;.deGH;NP6H)03b9�GHd_6HC2Ct+.-I;.9<9�GH70+./2P /E¥@68+./EGR)+:9@3N-D)0/2�XBI9@1NPAWl6HJ0J0/2)0U�)IGR/21.9�+:GQ+.-09�1.WX)A+.-I9<+./23�[email protected];.9@PQ9@)A+kJ068+.6Q1.B035-?+.-D68+�+.-I9 � ��� � �!� J�*}{1:9<9 +T/EURBI;.9@1 >A\ � }{3m��6H)DJ#>A\ "R�5\>Sk-I9>;.9@3bGR)01:+:;5B03b+./EGR)§70;.G][email protected]�=`6H1f1.+.68;.+:9@JZdn;NGRP�6H)Z/2)D/E+./26HC�[email protected]����!?+.-D68+=`6H1�� � � -0/2UR-I9<;Q+.-06H)¤+.-09~1.3<68+:+:9<;N/2)0UK3bGA9��?3</E9@) + GHd�+.-09^PD6H3��XUH;.GRB0)DJ¤PQ9@J0/2BDP }{1:9<9+T/EURBI;.9@1 >A\ >]} Pp��6H)0J >A\ � �5\

Sk-I9QC2Pji * + g �MPQ9<+.-IG]JM+:GXG�� � ¨ PD6H1./23jGH7c9<;N68+./2GR)01} ¨ � � ¨ �R�F6H)0JM+.-I9 * + g �,PQ9<+.-IG]J)I9<9@JI9@J 5 ¨ PD6H1./23FGH7p9<;568+./EGR)01j} � "� ¨ �R�5^�=L/E+.-�CEGHU & � }��� � �.- ��� � " 6H)0J§CEGHU & � }��� � �.- ��� � �X^c;.9@1:7c9@3 i+./E�H9@CEWH\�Sk-09aC2GR)IUH9@1:+Q;.9@3bGR)01.+:;NB03b+./EGR)[+./2P9l=�6H1Q;.9@�XB0/E;N9@J PXW¦+.-I9 � g PQ9<+.-IG]J[=L/E+.- 5 ��� PD6H1./23GH7c9<;N68+./EGR)01�}�� � � � � �R�?6H)0J¤=L/2+.-¤CEGHU & � }��� � �/- ��� � .X\'SL-I9VG=P��:9@3b+./E�H9~d{B0)03b+./2GR)0168;.9§1.-IGm=�)¤/2)+T/EURBI;.9 >A\ ¨H¨ \kSk-I94;.9@3bGR)D1:+:;NB03b+:9@J�/2P68UH9@1�68;.9F1.-IG =L)~/Y) +T/EURBI;.9!>A\ ¨ � \kSL-I9F/2P68UH9�6H3<3<BI;N6H3bWV=�6H1-0/EUR-09@1:+�dnGH;L+.-I9 � PQ9<+.-IG]J014}{1:9<9>S_67PDC29�>A\ ¨ �5\

Page 16: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ �!� ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

0 100 200 300 400 500−2.1

−2

−1.9

−1.8

−1.7

−1.6

−1.5

−1.4

number of function and gradient evaluations

obje

ctiv

e fu

nctio

n lo

g 10(Φ

) [a

.u.]

CG method lm−BFGS methodBFGS method

+T/EURBI;.9 >A\ ¨H¨� � P��:9@3b+./E�H9�d{B0)03b+./EGR)01T1:+.68;N+./2)IU�dn;NGRP£6H)Q/2)0/E+./26HC [email protected] � ��! +.-068+&=�6H1 � � � -0/2UR-I9<;T+.-06H)+.-I9SPD6H3/�AUH;NGRB0)0JQ1.3<68+:+:9<;N/Y)IU4GHdp+.-I9�GH;N/EUR/2)D6HCAPQ9@JD/2B0P�\ '�J0JD/E+./EGR)06HC2C2WH^ +.-09k1:WX)A+.-I9<+./23�[email protected];.9@PQ9@)A+J068+.6Q=`9<;.9F3bGH;N;NBI70+:9@JdPXWa)IGR/21:9f=L/2+.-�6�� ��� GHd �!� J�*�\

Page 17: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨ �]¨

� � #�� ; ��� 204F8 $ 3 � B�2 � .� *+X /F��< / S 8 � � . � 20/@8 $�< Z

� / #%�@� " O � ; CK��� 204F8 $ 3� B 2 � . > 7 /;�:< / S 8 � � . � "20/@8 $F< Z

� �

� �� �� �

� S # O � ; C'��� 204F8 $ 3�� B�2 � . � 7 /;� "< / S 8 � � . � 20/@8 $�< Z

+T/EURBI;.9 >A\ ¨ �$� +T/2)D6HC�/2P68UH9�;.9@3bGR)01:+:;NBD3b+./EGR)01kGHd � � \�SL-I9F/2)0/2+./[email protected] � �"! =�6H1 � � � -0/EUR-I9<;L+.-06H)+.-I9yPD6H3/�AUH;.GRBD)0J�1.3<68+:+:9<;N/2)0UQGHd¡+.-I9�GH;N/EUR/Y)06HCtP9@J0/2B0P�\&Sk-09 � ��� GHd_+.-I9f1:WX)A+.-I9<+./[email protected];.9@PQ9@)A+J068+.6Q=�6H1 �!� J�*�\���/21:+.6H)03b9,Pc9<+ =%9<9@)�6HJ �:6H3b9@)A+L/21.GRC2/2)I9@1�/21 ¨ 3<P�� & \

� � #�� ; ��� 204F8 $ 3W� B 2 � .> 7 /F��< / S 8 � � . � 20/ 8 $F< � �/32 � . � 20/@8 $�<$# Z

� /#%�@� " O � ; CK��� 204F8 $ 3� B 2 � . > 7 /;�:< / S 8 � � . �:"20/ 8 $F< � 7L> /@2 � . � 20/@8 $�<$# Z

� �

� ���� �

� S # O � ; C'��� 204F8 $ 3�� B�2 � . > 7 /;�:"< / S 8 � � . � 20/@8 $�< � 7 � /32 � . � 20/@8 $F<$# Z

+T/EURBI;.9 >A\ ¨ � � (*P68UH9l;.9@3bGR)01.+:;NB03b+./EGR)01FGHd � � 68de+:9<; � ¨ PD6H1N/23QGH7c9<;N68+./EGR)01@\aSL-I9 /2)0/2+./[email protected] � �"!=�6H1 � � � -0/EUR-09<;�+.-D6H)Z+.-I9TPD6H3��XUH;.GRB0)DJM1.3<68+:+:9<;N/2)IU~GHd +.-I9QGH;N/2UR/2)06HCTPQ9@J0/2BDP�\FSk-I9�� ��� GHd`+.-I91:W]) +.-09<+./[email protected];N9@PQ9@) +�J068+.6Q=�6H1 �!� J�*�\���/21.+.6H)03b9,Pc9<+�=`9<9@)~6HJ �.6H3b9@)A+L/21:GRC2/Y)I9@1�/21 ¨ 3<P � & \

Page 18: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

)XB0P|Pc9<;�GHd 3bGH;.;.9@CY68+./EGR) JI9<�X/Y68+./EGR)9b�I6HPQ7DCE9 Pt6H1./23�GH7c9<;N68+./EGR)01 PQ9<+.-0GXJ 3bGX9�� 3</E9@)A+ ��� de6H3b+:GH; � /)IG)0GR/21:9 ��.�" � g � \ �!� � \ � �

. � C2PQi * + g � � \ � " � \ " 5¨ > � * + g � ������� �����

. � � g � \ ��. � \ > 5. � C2PQi * + g � � \ � " � \ " 5. � * + g � ����� � �����

�!� J * � ��� ���" � g � \ " > � \ � .� � C2PQi * + g � ������� ����� �� � * + g � � \ � ¨ � \ � �� � � g � \ "� � \ � >� � C2PQi * + g � ������� ����� �� � * + g � � \ � ¨ � \ � �

/2)D/E+./[email protected] � � � -0/EUR-I9<; 5 �]¨ � g � \ > � � \ > �� 5 C2PQi * + g � � \ > 5 � \ ��.�]¨ � * + g � ������� �����

� 5 � g � \ "� � \ � >� 5 C2PQi * + g � � \ > 5 � \ ��.� 5 * + g � ����� � �����

/2)D/E+./[email protected] � � � -0/EUR-I9<; 5 ��� � g � \65 " ¨ \ � 56H)0J �!� J�* � ��� � ¨ C2PQi * + g � ��� �������5 ¨ * + g � � \ " 5 ¨ \ � 5

� ¨ � g � \65.� ¨ \ �I¨� ¨ C2PQi * + g � ��� �������� ¨ * + g � � \ " 5 ¨ \ � �Sh67PDCE9 >A\ ¨� (*P 68UH9~6H3<3<BI;N6H3bW¦GHd�;N9@3bGR)01:+:;NB03b+:9@J�/2P68UH9@1jdeGH; 6HC2C`+.-I;.9<9�GH70+./YP/E¥@68+./EGR)¦+:9@3N-D)0/2�XBI9@1}�� g ^hC2Pji * + g �c^_6H)0J1* + g �0�5\h(*P68UH9@1�=L/E+.-"-0/EUR-I9@1.+46H3<3<BI;N6H3bWK68;.9?;.9<70;[email protected]@) +:9@J PAW,6�C268;.UH9 ���6H)0JV6 1.P6HC2C � / } PcGRC2JIix70;N/2)A+:9@Jt�5\

Page 19: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨ � ��� ��� �� � "�#,� ��#,#,"(��&

(*)D/E+./26HC2CEWH^]=`9F1:+.B0JD/E9@Ja+.-I9�/YPQ7D6H3b+�GHd&)IGR/21:9�/2PQ7cGR1:9@JaGR)~1.WX)A+.-I9<+./[email protected];.9@PQ9@)A+.1<\9�M9deGRB0)0J,+.-D68+>+.-09�* + g �¦P9<+.-IGXJ¦6H)0J"+.-I9aC2Pji * + g �"PQ9<+.-IG]J¦CE9@6HJ¦+:G§1.P 6HC2CE9<;F�86HC2BI9@1 �� GHdk+.-I9G=P��:9@3b+./E�H9�d{B0)03b+./EGR)"=L-I9@)[)IGM)IGR/21.9l/21>70;N9@1:9@) +Q/2)"+.-I9VPQ9@6H1NBI;.9@PQ9@)A+QJ068+.6]\�+0B0;.+.-I9<;NPQGH;N9H^�+.-I9 � P9<+.-IGXJD1�;N9@�AB0/2;.9@J~de9<=`9<;{PD6H1./23�GH7c9<;N68+./EGR)01�+.-06H)§+.-I9�� g PQ9<+.-0GXJ§+:G�1.68+./21:deWV+.-I9Q1:+:GH7D7D/2)IU3b;N/E+:9<;5/EGR)�\&Sk-I9 � g PQ9<+.-0GXJ�)I9<9@J09@Ja+�=L/23b946H1LP6H) WfPD6H1./Y3LGH7c9<;N68+./EGR)D14}{1:9<9 +T/EURBI;.9'>A\ � }{6 �:�5\�Sk-I9/2P68UH9§6H3<3<BI;N6H3bWH^�;.9<70;.9@1:9@)A+:9@J�PAW�+.-I9Z3bGH;.;.9@CY68+./EGR) 3bGX9�� 3</E9@)A+ ��� 6H)0J J09<�X/268+./2GR)¤d{6H3b+:GH; � / ^k/21-0/EUR-09@1:+�dnGH;L+.-I9#* + g �~6H)0J�C2Pji * + g �VPQ9<+.-IG]J01F}{1:9<9�S_67PDC29�>A\ ¨ �5\

Sk-I9�6HJI� 6H)A+.68UH9@1�GHd � P9<+.-IGXJD1 G �H9<;�� g PQ9<+.-IG]J01 =`9<;.9�J0/2P/Y)0/21.-I9@J>GR)03b9f)IGR/Y1:9L=�6H16HJ0JI9@J,+:G~+.-I9 [email protected];.9@PQ9@)A+FJ068+.6]\ '�C2CT+.-I;.9<9�}�� g ^¡C2Pji * + g �p^_6H)0J * + g �0�fP9<+.-IGXJD1f;.9@6H3N-09@J687070;NG@�I/2P68+:9@CEWM+.-I9a1.6HPQ9 D)D6HC��86HC2BI9 �� GHdk+.-I9lG=P��:9@3b+./E�H9adeBD)03b+./EGR)"dnGH;j6�� ��� 5 "8J�*�\MSk-I9/2P68UH9�6H3<3<BI;N6H3bWGHd¡+.-I9 D)D6HC0;.9@3bGR)01.+:;NB03b+:9@Jl/2P68UH9@1`/21 )IGH+`1./EUR)0/ D3<6H) +.C2WjJD/�op9<;N9@) +<\ ��Gm=`9<�H9<;@^I+.-I9C2Pji * + g �aPQ9<+.-IG]J�6H)0J$* + g �VPQ9<+.-IG]Ja=%9<;.943bGR)D1./2JI9<;N67PtCEWd{6H1:+:9<;k+.-06H)�+.-09�� g PQ9<+.-IG]J�\&Sk-I9<W)I9<9@JI9@J ¨�� +:G ¨ "Q+./2P9@1kde9<=%9<;aPD6H1./234GH7p9<;568+./EGR)01�+.-06H)�+.-I9 � g PQ9<+.-0GXJ¦}{1:9<9�+T/EURBI;N9@1 >A\ � }{3m��6H)0J>A\ � }{Jt�:�5\

Sk-I9 � PQ9<+.-0GXJ01L6HC21:GGRBI+:7c9<;.deGH;NPQ9@JV+.-I9 � g PQ9<+.-IG]JV/2)V3bGRPQ7tBI+.68+./EGR)06HC�1.7p9<9@J�6H)0J/2P68UH9�6H3<3<BI;N6H3bWQ=L-I9@) 1:+.68;.+./2)IUFdn;.GRP�J0/�oc9<;.9@) +%/2)0/E+./26HCXURBI9@1N1:9@1<\&Sk-I9�� g PQ9<+.-IG]J 6HCE=�6@W]1 )09<9@JI9@J+�=�/23b96H14P6H)AWjPD6H1N/23>GH7p9<;568+./EGR)01�+.-06H)M+.-09 � PQ9<+.-0GXJ01@\��~GH;.9<Gm�H9<;@^h+.-I9 * + g �,PQ9<+.-IG]JM6H)0J+.-I9lC2Pji * + g �,PQ9<+.-IG]J,deGRB0)0J,1.P 6HC2CE9<;4�86HC2BI9@1FGHd �� +.-06H),+.-09 � g PQ9<+.-IG]J,;[email protected]+./2)IU�/2)M;N9@3bGR)]i1:+:;NBD3b+:9@J>/YP68UH9@1h=L/E+.->-0/EUR-I9<;T/2P68UH9�6H3<3<BI;N6H3bWa}{1:9<9�S_67PDC29 >A\ ¨ �5\ �M9�deGRB0)0J�+.-068+_+.-09 � PQ9<+.-IG]J011:GRPQ9<+./YPQ9@1�d{6H/2C�/2)a3<6HC23<B0C268+./Y)IU6Q1:9@68;N35-~J0/E;N9@3b+./EGR)a+:Gm=�68;NJ01k6 P/2)0/2P>B0P�^X/Ed¡+.-09F/2)0/E+./Y6HCDURBI9@1N1 � ���GHdh+.-I9F1.3<68+:+:9<;N/Y)IU3bGA9��?3</E9@) +�/21�d{68;�dn;.GRP�+.-I941:GRC2BI+./2GR)�\&(*)a+.-D/21�3<6H1:94+.-I9�687070;.Gm�]/2P 68+:9@J �[email protected]/26H)P/EUR-A+�)0GH+|Pc9aJI9 D)I9@JKGH;>+.-09l1:9@68;53N-[J0/E;.9@3b+./2GR)KP6mW")IGH+nPc9?6§[email protected]@)A+>J0/2;.9@3b+./EGR)�\§Sk-I9<;.9<deGH;.9H^+.-I9 �L9@1N1./26H)'P68+:;N/��¤=�6H1�6HBI+:GRP68+./Y3<6HC2CEW¤;.9<7tC26H3b9@J PXW¤+.-I9M/2J09@) +./E+ W¤P68+:;N/���6H)0J�=`9Z9@)IdeGH;N3b9@J7cGR1./E+./E�H9bi�J09 D)0/E+:9@)I9@1N1<^A+.-09<;.99PAWaG=P0+.6H/Y)0/2)IUQ6JI9@1N3b9@) +L1.9@68;N3N-�J0/E;.9@3b+./EGR)�\

Page 20: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � 5 ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� Sk-I9lP6 �vGH;JD/21.6HJI�86H) +.68UH9lGHdL+.-09�* + g �¦P9<+.-IGXJ[/21>/E+.1jC268;.UH9aPQ9@PQGH;NW,;.9@�XB0/E;.9@PQ9@)A+<\

� BI;41.+.B0JIW�1N-IGm=L14+.-068+4+.-0/21fJD/21.6HJI�86H) +.68UH9?3<6H) Pc9Q6HC2CE9<�]/268+:9@J`PXW§/2P7DCE9@PQ9@)A+./2)IUl+.-I9 C2PQi * + g �PQ9<+.-IG]J�\aSk-I9 CYPji * + g �M6HC2UHGH;N/E+.-0P ;.9@�ABD/E;.9@[email protected]�PQ9@PQGH;.WZ+.-06H)K+.-I9 * + g �,6HCEUHGH;5/E+.-0P�^_=L-0/2CE9+.-I9>/2P68UH9��XB06HC2/2+�Wa6H3N-0/E9<�H9@J§=L/2+.-�+.-I9�CYPji * + g �V+:9@3N-0)0/Y�ABI9H^t=`6H1�687070;NG@�I/2P68+:9@CEWa9@�XB06HC�+:G?+.-068+G=P0+.6H/2)09@J�=L/E+.-a+.-I9#* + g �VPQ9<+.-0GXJK}{1.9<9FS_67PtCE9�>A\ ¨ �5\

(*)�3bGR)03<C2B01N/EGR)�^ +.-I9 � P9<+.-IGXJD1�GRBI+:7c9<;.deGH;NPQ9@JF+.-I98� g PQ9<+.-0GXJ�/2)4+.-I9`3bGRPQ7DBI+.68+./2GR)06HC1:7c9<9@JMGHd D)DJ0/2)IUa+.-I9 P /2)0/2P>B0P GHd�+.-I9G=P��:9@3b+./E�H9ldeBD)03b+./EGR),6H)0JK/2),/2P68UH9l6H3<3<BI;N6H3bWH\ � )DCEW~deGH;[email protected];.9@PQ9@)A+�J068+.6f=L/E+.-Q6 � ����� 5 "8J�*[+.-I9 � PQ9<+.-IG]J01�6H35-0/E9<�H9@J6F1./EUR)0/ t3<6H) +&-0/EUR-09<;�/2P68UH96H3<3<BI;N6H3bW§6H)0J~6l1.P6HCYCE9<;L�86HC2BI9 �� \�Sk-I9 � PQ9<+.-IG]J01�)I9<9@JI9@J�dn9<=`9<;yPD6H1./234GH7p9<;568+./EGR)01<^qPc9@3<6HB01:96H)a687070;.Gm�]/YP68+./EGR)?+:G�+.-I9�/2)A�H9<;N1:9��L9@1N1./26H)ldnGH;�3<6HC23<B0CY68+./2)IUF+.-09�1:9@68;53N-�J0/E;N9@3b+./EGR)?6H)DJ?6H)a/2)I9b�I6H3b+C2/2)09F1:9@68;N35-Z=%9<;.9QB01.9@J�\�(v)§3bGR) +:;N6H1.+<^�+.-I9�� g PQ9<+.-IG]J�)I9<9@J09@J§PGH;.9|Pt6H1./23�GH7p9<;568+./EGR)01<^c1./2)03b9>/E+;.9@�XB0/E;.9@JK6H),9b�I6H3b+>C2/Y)I91:9@68;N35-�}{C2/Y)I9bi�P/2)0/YP/E¥@68+./EGR)t�k+.-068+>B01:9@J,PQGH;N9 deGH;.=`68;5JK3<6HC23<B0CY68+./EGR)01fdeGH;9@6H3N-�UH;N6HJ0/29@) +k3<6HC23<BDC268+./EGR)�\

����� ��� ���&���k�� ������p����� � ��� � ����� ������� � �

Sk-I9VG=P��v9@3b+./E�H9Zd{B0)03b+./EGR) 6HC21:G¦JI9<7c9@)0J01QGR)�+.-I9§)AB0P|Pc9<; � GHd41:GRBI;N3b9bi�JI9<+:9@3b+:GH;�7t6H/E;N1}{1:9<9 ��9 D)D/E+./EGR) "X\ ¨ �Q6H)DJ�+.-I9@/E; 1.7D68+./26HC�7cGR1./E+./EGR)D1<\ �`GR)01:9@�XBI9@)A+.CEWH^%+.-09~JI9<;N/E�868+./E�H9V3<6HC23<BDC268+./EGR)6HC21:GVJ09<7p9@)DJ01�GR)M+.-I91:GRB0;N3b9bi�JI9<+:9@3b+:GH;Q3bGR) 0URBI;568+./EGR)�^�=L-D/23N-MCE9@6HJD1f+:G~J0/�oc9<;.9@)A+�;.9@3bGR)01:+:;NBD3b+./EGR);[email protected]+.1fGHd � � 6H)0J � � \ ��9@)03b9H^h=%9 7p9<;NdnGH;NP9@J,6V1:+.B0J0W�GR)"6V1./2PQ7tCE9j+:9@1:+�PQ9@JD/2B0P +:GV9@1:+./YP68+:9-IG =�P6H)AWa1.GRBI;N3b9@1k6H)0J~JI9<+:9@3b+:GH;N1�=%9<;.9�)I9@[email protected];.Wl+:GW]/E9@C2J�6QUR/2�H9@)V/2P68UH9F6H3<3<B0;N6H3bWH\

�� �� �� ��� �� *(%+� � % ����� � ��& '! % �#" � '

�M9L-06m�H9L3N-IGR1.9@)6H)Q9b�I6HPQ7DCE9�+.-068+�3bGR)A+.6H/2)01�+.-I;.9<9LJ0/Eop9<;.9@)A+&1.3<68+:+:9<;N/2)0U4-I9<+:9<;.GHUH9@)I9@/E+./29@16H1`1.-IGm=�) /2) +h/2URBI;.9 >A\ ¨ 5I\ SL-I9kGH70+./23<6HCD7D68;N6HPQ9<+:9<;51%GHdc+.-I9ZPDB0C �jPQ9@J0/YB0P£=`9<;.9 ��$ � ¨H¨�� ��3<P � & ^�&% � ��� ��"�3<P�� & ^46H)0J(' � � \�Sk-09M+.-I;.9<9K1.3<68+:+:9<;5/2)IU¤7c9<;.+.BI;HPD68+./EGR)01�-06HJ +.-I9,7D68;N6HP9<+:9<;N1

Page 21: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨ � "

��$ � " ��� 3<P�� & ^,��$ � ¨ > � 5f3<P�� & ^R6H)0J ��$ � � � � � 3<P � & \TSk-I9`67PD1:GH;.7D+./EGR)�3bGX9�� 3</E9@)A+hGHd0+.-I9`+.-I;.9<97c9<;.+.BI;(Pt68+./EGR)01p=`6H1_)IGH+�6HCE+:9<;.9@J�\

���

� �� �� �

+T/EURBI;.9 >A\ ¨ 5 � �]3<68+:+:9<;N/2)0U,3bGA9�� 3</29@) +.1 � � GHd�GH;N/EUR/2)06HC`PQ9@J0/YB0P =�/E+.-[J0/2PQ9@)01N/EGR)01��§3<P��1�§3<P3bGR)A+.6H/2)0/2)IU�+.-I;.9<9a-I9<+:9<;.GHUH9@)I9@/2+./E9@1�} ��$�� " ��� 3<P�� & ^ ��$�� ¨ > � 5M3<P�� & ^&6H)0J ��$�� � � � � 3<P�� & �5\Sk-I9��tB0C � PQ9@JD/2B0P -06HJV6Q1N3<68+:+:9<;N/2)IU 3bGX9�� 3</E9@)A+ � $ GHd ¨H¨�� � 3<P�� & \�� �� �� &������������� � "� % � %+&�� : � � % � # �� �� � ��� � %�� � % �)%+���)�&� � � " � #

+IGH;�6HC2CA;.9@3bGR)01:+:;5B03b+./EGR)01h=`9�BD1:9@J>9@/E+.-I9<; 5I^ � ^RGH; ¨ � 1:GRBI;N3b9@1<^ =L-0/235-F=`9<;.9�1:W]PPQ9<+:;N/23<6HCYCEW7cGR1./E+./EGR)09@J�68;.GRB0)0J�+.-09FPQ9@J0/2BDP�\�Sk-I94)XB0P�p9<;�GHd&JI9<+:9@3b+:GH;51�3bGR)01N/21:+:9@JVGHd&1:9<+.1LGHd ¨ � ^ � � ^ "�X^tGH;¨ � �j+.-068+�=`9<;.9f6HC21:GQ7tC26H3b9@J�1:W]PPQ9<+:;N/23<6HCYCEWQGR)�6HC2CcdeGRBI;�1./2JI9@1`GHdh+.-I9fPQ9@J0/2B0PV\TSL-I9<;.9<deGH;.9H^I+.-I9 ¨ �7cGR1.1./��tCE9�1:GRB0;N3b9bi�JI9<+:9@3b+:GH;L3bGRP�D/2)068+./2GR)01�;[email protected]+:9@J?/2)l;.9@3bGR)D1:+:;NB03b+./EGR)D1�6H1�1.-IGm=�)l/Y) +T/EURB0;.9@1 >A\ ¨ "X^>A\ ¨ �X^ >A\ ¨ >A^�6H)0J�>A\ ¨ � \~Sk-I9UH;56@W]1.3<6HCE9lGHd�+.-I9?/2P 68UH9@1�3bG �H9<;N1>+.-I9 ;N6H)0UH9 de;.GRP � $ � "V3<P � & +:G��$ � � 5 3<P � & \�Sk-I941N3<68+:+:9<;N/2)IU 3bGX9�� 3</E9@)A+��c9<+�=`9<9@)~6HJ�:6H3b9@)A+�/21.GRC2/2)I9@1�/21 ��$ � � 3<P � & \

Sk-I9Z/2P68UH9Z6H3<3<BI;N6H3bW�GHdF+.-I9Z;.9@3bGR)D1:+:;NB03b+:9@J'/2P68UH9@1a=�6H1�JI9<+:9<;NP /2)I9@J �AW�B01./2)IU"+.-I9JI9 D)D/E+./EGR)01�GHd�+.-I9 3bGH;N;.9@C268+./EGR)"3bGA9�� 3</29@) + � � }{1.9<9�� �XB068+./EGR) >A\ ¨ �46H)0J,+.-I9?JI9<�]/268+./EGR),de6H3b+:GH; � /}{1:9<9 � �XB068+./EGR) >A\65A�5\%Sk-09�3bGH;.;.9@CY68+./EGR)?3bGX9�� 3</E9@)A+.1�6H)0J?+.-I9�J09<�X/268+./2GR)d{6H3b+:GH;N1�68;.9�UR/E�H9@)?/Y) Sh6��DCE9>A\ � \)' C268;.UH9F� 6HC2B09fGHd ��� 6H)0JV6 1.P6HC2Cc�86HC2BI9�GHd � / /2)DJ0/23<68+:9@1�6-0/2UR-�/2P68UH946H3<3<BI;N6H3bWH\

Page 22: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u�

��� #���������� ��� � � / #����������� � � �

� �

� ������� �

�� #�� � �������� � � �

+T/EURBI;.9 >A\ ¨ " � (vP68UH9V;.9@3bGR)D1:+:;NB03b+./EGR)D1GHd � � =L/2+.- ¨ � JI9<+:9@3b+:GH;N1@\ ��/21.+.6H)03b9 �c9<+�=`9<9@) 6HJ�:6H3b9@)A+/21:GRCY/2)I9@1�/21 � 3<P�� & \

��� #����������� � � � � /#���������� ��� �

� �

� �� �� �

�� #�� � �������� � � �

+T/EURBI;.9 >A\ ¨ � � (vP68UH9V;.9@3bGR)D1:+:;NB03b+./EGR)D1GHd � � =L/2+.- � � JI9<+:9@3b+:GH;N1@\ ��/21.+.6H)03b9 �c9<+�=`9<9@) 6HJ�:6H3b9@)A+/21:GRCY/2)I9@1�/21 � 3<P�� & \

Page 23: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨ � >

��� #���������� ��� � � / #����������� � � �

� �

� ������� �

�� #�� � �������� � � �

+T/EURBI;.9 >A\ ¨ > � (vP68UH9V;.9@3bGR)D1:+:;NB03b+./EGR)D1GHd � � =L/2+.- "�MJI9<+:9@3b+:GH;N1@\ ��/21.+.6H)03b9 �c9<+�=`9<9@) 6HJ�:6H3b9@)A+/21:GRCY/2)I9@1�/21 � 3<P�� & \

��� #����������� � � � � /#���������� ��� �

� �

� �� �� �

�� #�� � �������� � � �

+T/EURBI;.9 >A\ ¨ �$� (vP68UH9l;.9@3bGR)01:+:;NBD3b+./EGR)01�GHd � � =L/E+.- ¨ � �~JI9<+:9@3b+:GH;51<\ ��/Y1:+.6H)03b9 �p9<+ =%9<9@)�6HJ�:6H3b9@)A+/21:GRCY/2)I9@1�/21 � 3<P�� & \

Page 24: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� �� �� 8 � "�#,� ��#,#,"(��&

��GXG��X/Y)IU�68+&Sh6��DCE9 >A\ � =%9`dnGRBD)0JF+.-D68+h+.-09�/YP68UH9`6H3<3<B0;N6H3bW>/Y)03b;.9@6H1:9@J�=L-I9@)>+.-I9�)ABDP �c9<;GHdD1:GRB0;N3b9bi�JI9<+:9@3b+:GH;&7D6H/E;51�=�6H1h/Y)03b;.9@6H1:9@J�dn;NGRP � ��5 � ¨ � }3+T/EURBI;N9 >A\ ¨ "I}{6 �:�h+:G � � � � "�>}3+h/2URBI;.9>A\ ¨ >]} �p�:�5\ '[d{BI;.+.-I9<;_/2)03b;.9@6H1:9`/2)f+.-I9`)ABDP �c9<;¡GHd01.GRBI;N3b9bi�JI9<+:9@3b+:GH;:ix7t6H/E;N1hJ0/2J4)IGH+h1.-IG =¦6�1./EUR)0/ t3<6H) +/2PQ7D;.Gm�H9@PQ9@)A+kGHdT+.-I9F/YP68UH9F6H3<3<BI;N6H3bWH\�Sk-09 �c9@1:+�;[email protected]+.1�=%9<;N94G �0+.6H/2)I9@JV=L/E+.- � 1.GRBI;N3b9@1L6H)DJ "�JI9<+:9@3b+:GH;N1�}3+h/2URBI;.9 >A\ ¨ >]} �p�:�5^AdeGRC2CEG =%9@J �XW ¨ � 1:GRBI;53b9@1&6H)0J ¨ � ��J09<+:9@3b+:GH;N1L}3+T/EURBI;.9 >A\ ¨ � }{3m�:�5^]6H)0J ¨ �1:GRBI;53b9@1�6H)0J'"��J09<+:9@3b+:GH;N1`}3+T/EURB0;.9 >A\ ¨ >]}{3m�:�5\

)XB0P �c9<;�GHd )ABDP �c9<;�GHd )AB0P�c9<;�GHd 3bGH;N;.9@C268+./EGR) JI9<�]/268+./EGR)1:GRBI;53b9bi�JI9<+:9@3b+:GH;�7t6H/E;N1 � 1:GRBI;N3b9@1 JI9<+:9@3b+:GH;N1 3bGX9�� 3</E9@)A+ � � de6H3b+:GH; � /5 � 5 ¨ � � \ � � � \ >..� � ¨ � � \ � � � \ > �¨ 5 5 ¨ � ¨ � � \ > � � \ > �¨H¨ � 5 � � � \ � > � \ >"� � 5 � � � � \ > � � \ >!�� �� ¨ � � � � \ > ¨ � \ > �� � 5 5 "� � \ > � � \ > 55 5 � � "� ����� �������� > � ¨ � "� ����� � �������

" � 5 5 ¨ � � � \ > � � \ >!�¨�� ��� � ¨ � � � \ ��. � \ >!�¨ " ¨ � ¨ � ¨ � � ������� �������

Sh6��DCE9 >A\ �$� (*P68UH9k6H3<3<B0;N6H3bW�GHdt;.9@3bGR)01:+:;5B03b+:9@J/2P68UH9@1 �XW�BD1./2)IU�J0/�oc9<;.9@)A+h1:GRB0;N3b9bi�JI9<+:9@3b+:GH;%3bGR) 0U8iBI;N68+./2GR)01<\ Sk-09f+.-I;.9<94;.9@3bGR)D1:+:;NB03b+:9@J�/2P68UH9@1k=�/E+.-a+.-I9F-0/2UR-I9@1:+k/2P68UH9�6H3<3<BI;N6H3bWV68;.94;N9<70;.9@1:9@)A+:9@J�XWl6CY68;.UH9 ��� 6H)0JV61.P 6HC2C � / } �cGRC2J]ix70;5/2) +:9@Jp�5\

�LG =%9<�H9<;m^A6H)Q6��D1:GRCYBI+:9�)AB0P�c9<;TGHdt1:GRBI;53b9bi�JI9<+:9@3b+:GH; 7D6H/2;N1<^8=L-0/235-j3<6H) �p9�68707DCY/E9@JFUH9@)09<;:i6HC2CEWQ+:Gj1.3<68+:+:9<;N/Y)IUQPQ9@J0/26]^]3<6H)a)IGH+ �c9�UR/E�H9@)�\�Sk-09�)XB0P �c9<;`GHd¡1:GRBI;53b9bi�JI9<+:9@3b+:GH;k7D6H/E;51�=L/2CYC06HCE=�6@W]1JI9<7c9@)0J"GR)¦+.-I9?7t68;.+./23<B0C268;j1.3<68+:+:9<;N/Y)IUMPQ9@J0/2B0PV^h/|\ 9H\M/E+.1>GH70+./Y3<6HC%7t68;N6HPQ9<+:9<;N1Q6H)0J"UH9<GRPQ9<+:;N/Y3<6HC

Page 25: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� ¨ � .

J0/2P9@)01./EGR)01@\( +�/21�/2)A+:9<;.9@1:+./2)0U�+:G)IGH+:9�+.-068+�6H)�/2)D3b;.9@6H1:9�/2)l+.-I9f)AB0P�c9<;%GHdhJI9<+:9@3b+:GH;N1�=�/2C2CD)0GH+`;[email protected]+

/2)>6�CY68;.UH9<;&3bGRPQ7DBI+.68+./EGR)D6HCA+./YPQ9H\ ��Gm=`9<�H9<;@^X/2)03b;.9@6H1./Y)IUk+.-I9�)ABDP �c9<;hGHdD1:GRBI;N3b9@1&/Y)03b;.9@6H1:9@1hC2/2)I9@68;5CEW+.-I9j6HPQGRB0)A+�GHd 3bGRPQ7DBI+.68+./2GR)06HCh+./2PQ9j)I9<9@JI9@J�dnGH;�7c9<;.deGH;NP/2)IU ;.9@3bGR)01:+:;NBD3b+./EGR)01<\�Sk-I9<;.9<deGH;.9H^�/E+�/211.BIUHUH9@1.+:9@J,deGH;F70;N68URP 68+./23j;.9@6H1:GR)01F+:G~B01:9Q+.-09 C268;.UH9@1:+�6HPQGRB0)A+4GHd�JI9<+:9@3b+:GH;N14+.-D68+�68;.9 6m� 6H/YC26��DCE9deGH;4G �0+.6H/2)0/Y)IUl/YP68UH9@1f=L/E+.-M-D/EUR-I9<;46H3<3<BI;N6H3bWH\?Sk-I9Q)ABDP �c9<;fGHd�1:GRBI;N3b9@14BD1:9@JM/21fC2/2P /E+:9@J �AW§+.-I93bGRPQ7DB0+.68+./EGR)06HC�;[email protected];N3b9@1k68+�-06H)0J�\

����� � � � ����������

(*)���-0687D+:9<; 5l=`9>7c9<;.deGH;NPQ9@J§6H)§9b�X7c9<;N/YPQ9@) +.6HCh1:+.B0J0WVGR)Z6?1.3<68+:+:9<;5/2)IUa7D-06H)A+:GRP�+.-068+3bGR)A+.6H/2)I9@J[6V�HGR/2JIi�C2/ �H9 ;5/2)IUI\ �M9a3bGRPQ7D68;.9@J¦+.-I9?9b�X7c9<;N/YPQ9@) +.6HC`J068+.6�=L/E+.- DBI9@)03b9?70;.G DCE9@1FG �Ii+.6H/2)I9@Jl=L/2+.-?+.-09�deGH;.=�68;NJ�PQG]JI9@C �D6H1:9@JaGR)a+.-I9 � � Sf\ ��Gm=`9<�H9<;@^D=`9fJ0/2Jl)IGH+�WH9<+�;.9@3bGR)01:+:;5B03b+�+.-I9GH70+./23<6HCX7D68;56HPQ9<+:9<;N1hGHdt6��HGR/2J]i�C2/ �H9`PQ9@JD/2B0P �XW49@PQ7tCEGmW]/2)IU�+.-I9%+:;56H)01:7cGH;.+vix+.-I9<GH;.WAi �D6H1:9@J � � *`(.( �1.35-I9@PQ9H\ Sk-09<;.9<dnGH;N9H^A=`9�UH9@)09<;N68+:9@Ja1:WX)A+.-I9<+./23�[email protected];.9@PQ9@)A+%J068+.6jB01./Y)IUF6>)AB0P9<;N/23<6HCDPGXJI9@CDGHd¡61.3<68+:+:9<;N/Y)IUlP9@J0/2B0P +.-D68+�3bGR)A+.6H/2)I9@JZ6�HGR/YJ]i�C2/ �H9�;N/2)IUI\kSk-D/21k9b�I6HPQ7DCE9�=`6H1�1./YP/2C268;�+:Gl+.-I9>7D-06H)]i+:GRP B01.9@J¤/2) �]B �D1.9@3b+./EGR) 5I\ ¨ \ ¨ deGH;9<� 6HCYB068+./2)IUZ+.-I9VdeGH;.=�68;NJ�PQG]JI9@C|\[Sk-I9�J0/21.+:;N/��DBI+./2GR)KGHd�+.-I91.3<68+:+:9<;N/Y)IU§3bGX9�� 3</E9@)A+.1>=`6H1>;.9@3bGR)D1:+:;NB03b+:9@J �XW,B01./2)IU~+.-I9l1.WX)A+.-I9<+./[email protected];.9@P9@) +jJ068+.6�GHdk+.-I9GH;N/EUR/Y)06HC�PQ9@J0/2BDP�\

Sk-I9�+:9@1:+ P9@J0/2B0P#-06HJJD/2PQ9@)01./2GR)01¡GHd�5F3<P �#5�3<P�6H)0JQ3bGR) +.6H/Y)I9@J 6�;N/Y)IUf/2)j+.-I9k3b9@)A+:9<;=L/E+.-Q6H)?/2)0)I9<;�JD/26HPQ9<+:9<;�GHd ��� 5�3<P�6H)0J6f+.-D/23��])[email protected]&GHd ��� �F3<P�\&Sk-I9k1.3<68+:+:9<;N/Y)IUF3bGX9�� 3</E9@)A+ GHdc+.-I9�D6H3/�AUH;.GRBD)0JMPQ9@J0/2BDP�=�6H1 ��$ � " � 3<P�� & 6H)0JZ+.-I9Q+.-I96H)D/21:GH+:;.GH7XW~d{6H3b+:GH;F=�6H141:9<+f+:G ' � ����� \Sk-I9Z6��D1:GH;N70+./EGR)�3bGA9�� 3</29@) +a=�6H1�1:9<+a+:G �&% � ��� ��"[3<P�� & \ Sk-09�;N/Y)IU"-06HJ'6 ��$ � ¨ 3<P�� & ^�&% � ��� � �I¨ 3<P � & ^¡6H)0J ' � ����� \��M97tC26H3b9@J �l1:GRBI;N3b9@146H)DJ ¨�� JI9<+:9@3b+:GH;N1fGR)Z9@6H35-K1./2J09�GHd`+.-I9PQ9@J0/YB0P�\ Sk-D/2141:9<+vi�BI7"=L/2C2CT6HC21.G �c9 B01:9@J,CY68+:9<;FdeGH;F9b�]7p9<;5/2PQ9@)A+.6HC�1:+.B0J0/29@14/2) ��-D6870+:9<; � \ � }{1:9<9

Page 26: GWDGwebdoc.sub.gwdg.de/ebook/diss/2003/fu-berlin/2002/135/kap7.pdf · Xs cu ybz ybz q Ns y NwHr u{z @u{q|w8r u =L-I9

¨ � � ���Xs��cu�ybz��������� ybz q�Ns!% � y�NwHr� u{z���@u{q|w8r � y� ��% u� 1.35-I9@P68+./2346H)DJV1:GRBI;N3b9bi�J09<+:9@3b+:GH;�3bGR) DURBI;N68+./EGR)V/Y) +h/2URBI;.9 � \��jGR)~7D68UH9 ¨ ��"R�5\

�M9�UH9@)I9<;N68+:9@J?1:WX)A+.-I9<+./23�PQ9@6H1NBI;.9@PQ9@)A+�J068+.6 �D6H1:9@JGR)j+.-I9 � � Sf\HSk-I9 D)D/E+:9bi�J0/�oc9<;.9@)03b9UH;N/2Jl-06HJl6j1./E¥<9�GHd �]¨ � �]¨ UH;N/2J?7cGR/2)A+.1 =L/2+.-?6�UH;N/2J]ix7cGR/2)A+%1.9<7D68;N68+./EGR) <�� � <���� ��� � "j3<P�\ �M9B01:9@J ¨ �4J0/Y1.3b;.9<+:9kGH;NJD/2)068+:9@1 6H)DJ3bGR)01./2J09<;.9@J )IGR)Iix;.9<9@) +:;NW �cGRB0)DJ068;.W�3bGR)DJ0/E+./EGR)01@\ �M9�1:+.68;.+:9@J?+.-I9;.9@3bGR)01.+:;NB03b+./EGR)fGHd���� �XW�B01./2)IU�+.-I9!� g PQ9<+.-IG]J�=L/E+.-f6L-IGRPQGHUH9@)I9<GRB01_/2)0/E+./Y6HCmURBI9@1N1�� $ � � " � 3<P�� & ^' � ����� ^�6H)0J �&% � � ��� ��"l3<P � & \�Sk-I9>;.9@3bGR)01:+:;5B03b+./EGR)�70;.G][email protected]=�6H1�+:9<;NP/2)D68+:9@J�68de+:9<; � � 5 �D6H1./23GH7c9<;N68+./EGR)01j}�� ¨ .� ¨ "R�5\FSL-I9F;.9@3bGR)D1:+:;NB03b+./EGR)�;[email protected]+LdeGH; � � /Y1�J0/Y1:7DC26mWH9@J~/2) +h/2URBI;.9 >A\ ¨ .I} �p�5\fSk-I9J0/21.+.6H)03b9��c9<+�=`9<9@)~6HJ �.6H3b9@) +�/21:GRC2/Y)I9@1�/21 � $ � ¨�� 3<P�� & \

����#��� ����������� � � ��� �� ����

��� ��� ��������� ����� �)$�� � � �

���

� �� ���� �

� / #�� � �� ������� ����)$ �!� ����� ���"�#� �� ��� "

��� ��!$�� � �%���� ���� ��� �

+T/EURBI;.9 >A\ ¨ . � � ;5/EUR/2)06HC&PQ9@JD/2B0P 6H)0JK;.9@3bGR)01:+:;NBD3b+:9@JK/2P68UH9 GHdk1.3<68+:+:9<;N/2)IU�3bGA9�� 3</29@) +.1 � � \lSk-I9GH;N/EUR/Y)06HC%P9@J0/2B0P 3bGR) +.6H/Y)I9@J�6§�HGR/2J]i�C2/ �H9a;N/Y)IU~=L/2+.- ��$ � ¨ 3<P � & \KSk-I9 �DB0C �,P9@J0/2B0P -06HJ�61.3<68+:+:9<;N/Y)IU 3bGX9�� 3</E9@)A+ ��$ GHd " � 3<P�� & \���/21.+.6H)03b9 �c9<+�=`9<9@)~6HJ �.6H3b9@)A+�/21:GRCY/2)I9@1�/21 ¨�� 3<P � & \

Sk-I9��HGR/2J]i�CY/ �H9�;N/2)IU�/21&3<CE9@68;NC2WF�]/21./��DC29%/2)>+.-I9�;.9@3bGR)D1:+:;NB03b+:9@J/YP68UH9F}{1:9<9 +T/EURBI;.9 >A\ ¨ .I} �c�:�5\Sk-I9�1.P6HC2C29@1:+��86HC2BI9LGHd¡+.-I9L;N/Y)IU�/21���$ � ��� � >�3<P � & \T(v)?3bGR)D3<C2B01./EGR)�^ +.-I9 � � *`(.( � 1.3N-09@PQ9 �t6H1:9@JGR)M+.-I9�� � S /21f6��DC29Q+:G�;.9@3bGR)01:+:;NBD3b+4�HGR/2J,68;.9@6H1@\���)A+./2C&)IG =4^¡+.-D/21�=`6H1F)IGH+47cGR1.1./��tCE9>/Y) � S �AWB01./Y)IUQJ0/�o�B01./EGR)]ix+.-09<GH;.W i �t6H1:9@Jl;.9@3bGR)01:+:;NBD3b+./EGR)VPQ9<+.-IG]J01<\