Sayısal Analiz (MATLAB) - Cüneyt Aydın Ders Notları

8/10/2019 Saysal Analiz (MATLAB) - Cneyt Aydn Ders Notlar

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Ulge Bc ncycgncr eeg

DCXNCBUcrh da Hlrs Gitncr

Hi. Hr. Aglyt CUHEG

Unhz Xlogeo gevlrsetlse

stcgbun-2632


2/75

eghloenlr

@ere

Dctres enldnlre

Qcy Jirdctncr

Xldln Negllr Alber nldnlre

Hezenlr (Crrcys)

Vri`rcd Hcnncghrcg jchlnlr (ej-lgh , swetam

Hg`nlr (jir-lgh vl wmenl-lgh hg`nlre)

@rcjeo

Hisyc yczh rdc-ioudcJigoseyig hisycs inuturdc


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Ocygcoc

Hi cg, \., (2665), Xldln Ben`escycr Benednlre H

Nescgs Hlrs Gitncr, stcgbun.

Hlderln, M., (266


4/75

DCXNCB (DCX rex NCBirctucry)

mttp;//www.dctmwiros.aid/dctncbalgtrcn/

DCXNCB,yoslo plrjirdcgsn ber uy`uncdc ycz nd vl berheneher.

DCXNCBeg tldlneghloe ycp

, biyutncgh

rdc `lrloterdlylg Ucpt d z td `erhe vl otncr, blnertl `lrloterdlosezeg b

tcg dncr.

no incrco Jirtrcg hene enl yczncg DCXNCB, hcmc sigrc A e


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Dctncbhl mczr pri`rcdncr vcrh r. Bu pri`rcdncrc jigosvlrener.Dctncb jigoseyigncr gg ounncgd , dctldcteotloe y4j(x) jig

ounncgd ync zhl ter.rgl eg, c4seg(x) jigoseyigughc, seg jigoseyigu, x c `erhe) hl lrege mlscpncr? ounncga bu hl lre, rgl eg, bectcr. c hl lre seg jigoseyigugug ber ots hr (iutput).


6/75


Cvcgtckncr ;

Ounncgd oincyn ,

nlted sestlde uyudnunu u,

Qcyscn cgcnez e nldnlreghloe oincyn oncr,

Mczr jigoseyigncr (jugateig jenls),

@rgtnldl (vesucnezcteig) oincyn (`rcjeo ezed),

@\E `lne terdl oincyn ,

DCXNCB hlrnlyeaese (lxl; lxlautcbnl hisyc enl weg12 uy`un

Xiinbixls (Crc outuncr ) ;mczr pri`rcdncr!


7/75

DCXNCB/Aiddcgh weghiw (oidut plgalrlse)

A

(

Hegcdeo oidut sct r Mlr trn dct. e nld,

Hldi, pri`rcd cn trdc vb. D-jenl lVri`rcdncr g y


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DCXNCB/ Pirospcal ( cncg )

Pirospcalplgalrlse

Ctcgcghl e olg Pirospcal plg

cdcg g oid

Pirospcal, en`ene iturudhc ountd hl e olgnlreg tutunhuu c


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DCXNCB/ Crrcy Lhetir (Heze lhetr)

Dctres, vlotr vl scy ncr eeg lxaln zlnneeghloe lhetrhr

Hcmc gal ctcgcg ber

biyutncr estlgenhee

oe jcron beedhl rgtnlger;

77 iplg('c')wirospcal plgalrlseghl en`enehl e olg eoe olz toncgr.


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DCXNCB/ Xldln Oidutncr

ana Aiddcgh weghiwu tldeznlr.

anlcr n`ene iturudhc ctcgd td hl e olgnlre senlanlcr c Ucngzac c hle olgege senlr.hldi Dctncb hldisugu cn tr r.hctl @g-Cy-Un `rgtnlr (rgl eg, 30-Iat-266lxet Dctncb iturudughcg ocr.

mlnp Ucrhd dlgsg ccr.mlnp jYgc jYgc jigoseyigu mcooghc ben`e vlrer.scvl h c c hl e olgege h hisyc esdeynl dct uzcgt n incnich h c hl e olgege h hisycs ghcg `lre c r r.

Qcvl vl nich oidutncr , dctres vb. ycp ncr g ocyhlhendlse e


11/75

DCXNCB/ Xldln hisyc trnlre

*.d DCXNCB pri`rcd hisycncr

*.je` @rcjeo hisycncr vl @\Enlreg `rcjeo pcrcn

*.dctHl e olg vl dctres hisycncr

*.p prl-pcrslh psluhi-aihl hisycncr (bu hisyc`rgtnlgldlz cgaco pri`rcd incrco c r ncbener, ycge Dcn tr ncbener!)


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DCXNCB/Dctresnlreg @erendlse

Dctres vl vlotrnlr _ T o lne pcrcgtlznlre enl tcg dncg r.

Dctres vl vlotr `erdlgeg 1 jcron yinu vcrh r;

rgl eg;

C4_3 1 6

c4ni`(c)?lnslc4c?

lgh c

He lr hurudhc

cgncd ghch r;Burchc, c76oi unugu tldsen lhlr.

c4egput( ' berej c>6

c4ni`(c)?lgh ej c76

c4c?lgh c

Lnsl ycp s ounn


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DCXNCB/swetam,acsl ycp s swetam (hl e ter) ej ycpsgc blgzlr. Burchc hcmc io szln incrco blnhurudncrc `rl ygnlgherdl e nlde ycpnr. Bu ycp gg ounncgd acslèbeher?

swetam hurud acsl hurud3

e nld3acsl hurud2

e nld2itmlrwesl

e nld1lgh

rglo; ùg hlèsolgegeg, es ùgu inup indch gc ocrcr vlrdlo eeg ch gnr?anlcr,anaùg4egput( 'mcgè ùg4' , 's' )?swetam niwlr(ùg)

acsl {'pczcrtlse' , 'scne' , 'acrscdbc' , 'plrsldbl'hesp( 'e `g' )acsl {'audcrtlse' , 'pczcr' }hesp( 'XCXN!' )

lgh

Ounncgd oe eyl bc nhr.


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DCXNCB/swetam,acsl ycp s

Ounncga tcrcj ghcg `erenlg ber c436.2828


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DCXNCB/\y`uncdc-6) & (HU76)c4( 'Cae 2.bin lhl' )?

lgh

zd

ej (H]>6) & (HU>6)c4( 'Cae 1.bin lhl' )?

lgh

ej (H]76) & (HU>6)c4( 'Cae 8.bin lhl' )?

lgh

ds`bix(c, 'Bin`l9' )


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DCXNCB/\y`uncdc-:3 vl 2. giotcg g ] vl U oiirhegctncr gg `erendlseghlg sigrc, (3-2)c onono c s g mlscpncycg ber pri`rcd ycz gz.

anlcrana]34egput( ']34' )?U34egput( 'U34' )?]24egput( ']24' )?U24egput( 'U24' )?H]4]2-]3?HU4U2-U3?

ej (H]~46)&(HU~46),c4ctcg(HU/H])?c4c*266/pe?ej (H]76)&(HU76),c4c? lgh

ej (H]>6)&(HU76),c4c+266? lgh ej (H]>6)&(HU>6),c4c+266? lgh ej (H]76)&(HU>6),c4c+866? lgh

lgh

ej (H]446)&(HU76),c4366? lgh

zd

H oi un

ej (H]446)&(HU>6),c4166? lgh ej (H]746)&(HU446),c46? lgh ej (H]>6)&(HU446),c4266? lgh

c%vlyc iutput c, c c hcoe beedhl yczh r ncbener.jpregtj( '%s%3.


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DCXNCB/\y`uncdc-03 vl 2. giotcg g ] vl U oiirhegctncr gg `erendlseghlg sigrc, (3-2)c onono c s g vl (3-2) olgcr uzugnu ugu mlscpncycg ber pri`rcd yc

anlcrana]34egput( ']34' )?U34egput( 'U34' )?]24egput( ']24' )?U24egput( 'U24' )?H]4]2-]3?HU4U2-U3?

ej (H]~46)&(HU~46),c4ctcg(HU/H])?c4c*266/pe?ej (H]76)&(HU76),c4c? lgh ej (H]>6)&(HU76),c4c+266? lgh ej (H]>6)&(HU>6),c4c+266? lgh ej (H]76)&(HU>6),c4c+866? lgh

lgh

ej (H]446)&(HU76),c4366? lgh ej (H]446)&(HU>6),c4166? lgh ej (H]746)&(HU446),c46? lgh ej (H]>6)&(HU446),c4266? lgh

Q4sqrt(H]W2+HUW2)? %olgcr

jpregtj( '%s%3.


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DCXNCB/\y`uncdc-5Ounncgay,3e sldlse hurudughc UX wlb scyjcsegc, 2ye sldlestlheegez ber wlb scyjcsegc ygnlgherlg ber dlg pri`rcd yc

anlcranahesp( '_3T...UX\ wlb scyjcse' )hesp( '_2T...Aglyt Cyh g wlb scyjcse' )c4egput( '>Qlnlateig74' )?

ej (c72)|(c>46) dlgu %Ounncg a g g 6,gl`ctej vlyc 1hlg byo scylgh hurudughc, pri`rcd ylgehlg bc nctdco eeg

ej c443 wlb www.yenhez.lhu.tr -briwslr

zd

lgh ej c442

wlb www.yenhez.lhu.tr/~acyheg -briwslr

lgh


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DCXNCB/jir,lgh hg`sjir,lgh hg`s ber e nldeg berhlg hcmc jcznc scyhc ycpt r ndcs gh(rgl eg, oo bundc pribnldnlreghl ounncgncg etlrcsyig zdnlre).

jir e43;g (e Xcd scy (egtl`lr))e nld

lgh

beedeghlher.

rglo ; 3hlg Gyl ochcr incg scyncr g tipncd g ycpcg ber pri`rcd anlcr,ana

G4egput( 'ber scye `eregez4' )?scy46? %scycajir e43;G

scy4scy+e? %bereoedne (odnctej tipncd)

lgh scy


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DCXNCB/ wmenl,lgh hg`swmenl,lghhg`s, blnerne ber hurudug `lrlonl dlse hurudughc berhcmc jcznc scyhc ycpt r ndcs ghc ounncgnr.

higl46? wmenl higl446

e nld lgh

rglo ; 3hlg Gyl ochcr incg scyncr g tipncd g wmenl,lgh hg`spri`rcd h glned.

anlcr,ana G4egput( 'ber scye `eregez4' )?

scy46? e46?higl46? wmenl higl446

e4e+3? %ber galoe rglotl jir,lgh hg`sghloe e yl ocrej e44Ghigl43?

lgh scy4scy+e?lgh scy

3. Burchcoe, wmenl,lgh hg`s, higl hl cgaco 6 inhu u zcdcg cn cacot r.

2. Ber galoe sctrhc, higl hl e olge 6 inceeg wmenl,lgh hg`s cn r.

(wmenl, lgh hg`sg cn t rcg jcron cnhl egendlylaloter ).

e, sig scy yc (Gyl) unc tghc, higl hl e olgegl 6ctcg r. Bynlal, wmenlg inhuu sct rc `lnegheeghl, hi

eeg wmenl, lgh hg`s cn dcz (hg` signcg r). Vrhg`gg lgh sct r gg mldlg cnt ghcoe sctrhcg e nld(burchc, scy hl e olge aiddcgh weghiwhc yczh r nr


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DCXNCB/\yùncdc-36g scy hc ngg tlo tlo hzlntdlse vl stcghcrt scpdcs èrenheeghl enène ocbc mctcn inup indch g blnernlylg, ocbc mctcn nnlre (vcrsc) yczh rcg be

zd anlcr,anag4egput( 'inau scyese4' )?scy46?jir e43;g

v4egput( 'huzlntdl4' )?s4egput( 'stcghcrt scpdc4' )?ej cbs(v)74(1*s)

hesp( '--------------------------' )hesp(_egt2str(e) '. inau ocbc mctcne' T)hesp( '--------------------------' )scy4scy+3?OM(scy,3)4e?

lgh ej cbs(v)>(1*s)

hesp( '--------------------------' )hesp(_egt2str(e) '. inau girdcn'T)hesp( '--------------------------' )

lgh lgh ej scy446

hesp( 'Ocbc mctcne inau yio' )lgh ej scy76

hesp( 'Ocbc mctcne incg inaunlr' )OM

lgh


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DCXNCB/@rcjeo Dctncbhl `rcjeonlr je`url plgalrlseghl ezherener.

oe vl biyutnu ezed ycg s rc, outupscn oiirhegct sestldeghl hl bunugur (bco., pincr).

Cpses (])

I r h

e g c

t ( U )

U

[

oe Biyutnu Oiirhegct Qestlde Biyutnu Oiirhegct Q


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DCXNCB/@rcjeo Dctncbhl lg tldln ezed jigoseyigu pnit hur.

rgl eg, x46;6.3;< incg ber heze vlotr lnldcgncr gc ocr no, y4xjigoseyig hl lrnlre mlscpnct nsg.pnit(x,y) enl c c hcoe `rcjeo ezherener.

ezenlg rcjeeg zlycpdco ddoghr.

Bugug eeg Lhet p

n`ene glsgl (ezhereolz t oncgcrco blnerplgalrlseghlg estlgenycp ncbener.

Vriplrty Lhetir plgaltrn hl e eonee, oddoghr.

rgl eg, pnit(x,y,giotcncr loenhloex,y giotc ejtnlrege `sldbin enl e crltnl

Lhet pnit


49/75

DCXNCB/@rcjeo pnit(x,y, '-i' ) enl enène `rcjeo c c hcoe èbe inur.

C c hcoe ejchlntlorcrncy gz;

pnit(x,y, '-i' pnit(x,y, '-*' pnit(x,y, '-+' pnit(x,y, '-W' pnit(x,y, '-.'

Qz lhenlg `rcjeèbe sldbinnlrl dc

pnit jigoseyigu enrlgège hl e terd

pnit(x,y, 'r' ) pnit(x,y, 'o' ) pnit(x,y, 'b' ) pnit(x,y, '`' )


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DCXNCB/@rcjeo-Ocyhltdl vl oipycncdcezenlg `rcjeonlre ocyhltdlo eeg Jeùrl plgalrlseghloe Jenl dlgsQcvl Cs sllglonlre slener. @rcjeonlr, je` uzcgtn hisycncr incrco eocyhlhenernlr.

ezenlg `rcjeonlreg bc oc ber irtcdc cotcr ndcncr eeg, Lhet dlgsJeùrl sllgl e slener. (Git; Oipycncdcgg croc pncg rlgège cycrnIpteigs sllgl egl bco gz.)


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DCXNCB/@rcjeo- Cyg loslg tco d gc jcron `rcjeonlr

Cyg loslg tco d gc jcron `rcjeonlre ezherdlo eeg minh ig vl mounncgnr. Bu eoe oidut crcs gc ycz ncg mlr trn `rcjeeg ezede tco d ghc `stlrener.

rgl eg, yc4_3?3.2?2.8?8.


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DCXNCB/@rcjeo-@rcjeo yinuync ben`e rltdlrglo; yc4rcghg(3666,3) vl yb4rcghg(3666,3)*1 beedeghl eoeinu turcnd. ( rcghg jigoseyigu, blonlglg hl lre 6, stcghcrt scpdcs 3 ihcnd scy rlter). ycgg stcghcrt scpdcs 3, ybgeg stcghcrt scpdcs

Bu nnlreg, c vl b ocygconcr ghcg lnhl lhenheege vl hl stcghcrt scpdcncbendlheedezeh glned. Mcg`e n `rubugug hcmc ocnetlne inhuugu (stch o inhuugu) `rcjeo zlreghlg `rlbendlo eeg, ber galoe rglotloe mioidutncr g ounncgcrco bugncr ezherdlo yltlrne incacotr;

minh ig, pnit(yc), pnit(yb, 'r' ),minh ijj

Byn`stlrsj rhhincyscpdcinhuoincy

Git; sqrt(yb*yb/555) e nlde, yc gg hlglysln stcghcrt scpdcs g vlrlaloHlrs Gitncr ). Bu hl lreg 1ourcdscn stcghcrt scpdc hl lregl yco g incac


53/75

DCXNCB/@rcjeo-@rcjeo yinuync ben`e rltdlBer galoe rglotl ounncgncg yc vl yb nnlregeg berbernlreynl gcsn b`rdlo eeg,

pnit(yc,yb, '.' )

oidutugu ounncgdco yltlrneher.

n`ene `rcjcrcs ghc c(oirlncsyig

mldlg trltblonlglg h`rubc ene odlrolzeghl(hcerl beeoe n `roirlncsyig giotc bunultrcj ghc `


54/75

DCXNCB/@rcjeo-@rcjeo yinuync ben`e rltdlBer galoe rglotl ounncgncgyb nnlrege,yb42+1*yc+rcghg(3666,3beedeghl yc nnlregl bcn incrco rltlned. Bu hurudhc,

pnit(yc,yb, '.' )

enl inu turuncg `rcjeotlg yc vl yb nnlre crcsghcoe oirlncsyigug vcr`rnlaloter.


55/75

DCXNCB/@rcjeo-@rcjeo yinuync benè rltdlDmlghesneo uyùncdcncr ghc lg io ocr nc ncg pribnldnlrhlg bere hbeedeghloe ber hlgonldeg enène crcnotcoe oog (jigoseyigu s j r ycpcbundcotr. Qcyscn cgcnezhl ounncgncg Glwtig-Rcpmsig èbe ygtldnlryconc o hl lregl emteyc vcrhr. Bu yconc o hl lre bundco eeg rcjeoounncg n indcotch r. rgl eg,

J(x)4x 1+x2-


56/75

DCXNCB/@rcjeo-Bcsea Jetteg` Xiin

Ber dmlghes, ber incy `znlr vl `znld siguaughc lnhl ltte e nndctldcteosln l etneonlrnl concdcyc cn r. Bynlse l etneonlrl, oscacvlrener.Je`url plgalrlseghl ylr cncg Xiins dlgs eeghloe Bcsea Jetteg`zlreghloe x vl bugncrc ocr no `lnlg y hl lrnlrege ounncgcrco, bugny4j(x) pinegidugu tcg dncr. Bynlal inhuoc prcteo ber beedhl dihln

Burchc mctrnctndcs `lrlolg eoe giotc vcrh r;

(3) Llr giotc ejte (x,y) scy s uyhuruncg pinegidug benegdlylg scy sbunugcg jigoseyig ber lgtlrpincsyig pinegiduhur.

(Git; g. hlrlalhlg ber pinegidug g+3 chlt benegdlylge inhu ugu mctrncygz; hlrlalhlg ber pinegid? y4cx 8+bx1+ax2+hx+l her vl benegdlylg scy s


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DCXNCB/@rcjeo-Bcsea Jetteg` Xiin

x 6 3 2 1 8 Ootr74 Byo letter>4 Oo letter44 Letter~4 Let hlenher

Qldbinnlr

% Concdc `lterdl ejchlse_ T Dctres èrdl ejchlse( ) ghes vl hllr èrdl ejchlse4 Hleolg ctcdc ejchlse? Dctresnlrhl sctr cyrca.

Cyr ac, eeghl "4" bunugcg ber enldeg `stlrendldlse

; Oinig ejchlsecgs Hleolg ctcgdcd lg sig

enld eeg vcrscyncghl eolg esde (cgs wlr)

{ } Marl hezesex. che x ycp hezese

Qcbet tlrednlr

pe scys lps 2.2268l-63: scys e gj Qigsuz (blnersez) ejchlse

Xreìgidltreo Jigoseyigncr

se g, ais , t cg, a it Xre`. Jigoseyigncr

cse g, cais, ct cg, cait Xlrs Xre`. ejchlnlr

Ni`cretdeo Jigoseyigncr

n i` Hi cn ni`cretdclxp Lospigcgseyln

Negllr Alber Jigoseyigncr

h l t (x) Ber x dctresegeg hltlrdegcgt e gv( x) Ber x dctresegeg tlrset rcal(x) Ber x dctresegeg ezehe c`( x) Ber x dctresegeg ol`lg

lnldcgncr he c`( y) Ol`lgnlre, ber y vlotrgg

lnldcgncr incg ol`lg dctreszlris Qj r dctresigls Bernlr dctreselyl Bered dctresle ` zhllr vl zvlotr bundc


75/75

Dctncb M zn Lre ed O ncvuzu

Uczh rdc Jigoseyigncr

j pr e gt j Ber ejchlgeg yczhr ndcs spr e gt j Ber ejchlgeg ber ocrcotlr hezesegl

ctcgdcs he sp Ber ejchlgeg lorcg ots incrco

`stlrendlse

Ocrcotlr hezese jigoseyigncr

gud2st r ( x) Ber x scysg ber ocrcotlrlctcdc

st r 2gud( x) Ocrcotlr incg ber x scysg scy hllregl ctcdc

amcr ( c) c marlsege ber ocrcotlrlctcdcamcr ( s3, s2, ) s3,s2, ocrcotlrnlreghlg

ylge ber ocrcotlr hezeseinuturdc

n iwlr ( s) Ber s ocrcotlr hezesegeg tdlnldcgncr g oo mcrjycpdc

upplr ( s) Ber s ocrcotlr hezesegeg tdlnldcgncr g byo mcrjycpdc

e sgudlr e a Ber hleolgeg scy inupindch g sirùncdc

e samcr Ber hleolgeg ocrcotlrinup indchg sirùncdc

e saln n Ber hleolgeg marl inupindch g sirùncdc

Mcz r @\E'nlr

ds`bix nlte plgalrlsee gput hn ` Hllr èrdl plgalrlsequlst hn ` Qiru heycni` plgalrlse

ue `lt j e n l Iplg jenl heycni` plgalrlseue `lt he r Iplg herlatiry heycni` plg.\e put j e n l Qcvl jenl heycni` plgalrlse

Qcy yuvcrnctdc jigoseyigncr

Bcz dctldcteosln jigoseyigncr

sud( x) Ber x vlotr lnldcgncr ggtipncd

he j j ( x) Ber x vlotr lnldcgncr ggcrho jcroncghr ndcs

dlcg( x) Ber x vlotr lnldcgncr ggirtcncdcs

dlhe cg( x) Ber x vlotr lnldcgncr ggirtc hl lre (dlhycg )

s i r t ( x ) Ber x vlotr lnldcgncr ggootlg byl s rcncgdcs

dcx, de g Lg byo vl lg oo hllr bundc

sir t r iws nène stugc `rl ootlg byl s rcncdc

Vri`rcdncdc

e j / lgh Llr oi unuj ir / glxt Hg`wme n l/ lgh wmenl hg`se gput Hleolg èrherdl

ezed

pn it 2 biyutnu `rcjeopn it 1 1 biyutnu `rcjeome s t , bcr Mesti`rcd vl bcr `rcjeonlresur j , dlsm Uzly `rcjeonlrej e ùr l ezed plgalrlse inuturdc

(oe vlyc hcmc jcznc scyhcoe`rcjeonlre cyr plgalrlnlrhl`stlrdlo eeg)

min h ig,min h ij j

Jcron `rcjeonlre cyg loslgtco d ghc ezherdloidutncr

cxe s Loslg oidutucxe s lqucn Loslgnlre let nlo octscys

enl nlonlgherdlstld b ` j

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Sayısal Analiz (MATLAB) - Cüneyt Aydın Ders Notları