Maths 2118121

• HW #2 due 2,125 @ 9PM

•Read 3. I -3.3 for Tuesday

Find x such that fix)=Oin

non- linear

•tookouer2.l-2.SI

Condition and stability-

: Evaluate fan

¥¥¥¥*i:¥i¥Txmx*HIx⇒ K = OCI

) , well- conditioned

K >7 I ,Ill - conditioned

E± : fan= Txt- Tx , uniformly

well - conditioned

-

Kt Txt_rx=£¥c¥¥⇒

a) fan = Txt- Tx 4 -digit arithmetic

FCI 984 ) = ft - ifUNSTABLE

t.TT#xo2--0.4454xsubtractive -

cancellation= o .

ooo 1×102 = 0 . I 000 X to'

Fed's it

MATLFB-i.T-T4-0.1-39.i.XIO-I99.IR⑦ fan =#¥rxfa984)=oF¥¥ozFo.it#sxTFIyy5T.io--o.sgoeToi-"IIABLE

Evaluate fix,- +

\(

Y

well -conditioned Ill -conditionedI

Also:#\ABLE UNSTABLE

Ex : ax'tbxtC=o ⇒ x+,=-b±FX2A

a = O -

2MATLAB

Xt = 239.4247 . . . -6=-47.91 =3 -

c. = 6X-

= 0.1253 . . .. .

4-digitarithnet.ie subtractive

Xt,-re

To cancellation

2. (0.2)

a 41917¥23 f47.967,4285 ={¥÷¥

Ct)

~~ 0i)I-digit

Fix ? x-

tE÷÷÷4÷X-

=47.ci#FEEIoTI.e4IFsibO:l253nfall 4-digitaccuracy !

Floating Point Number Systems-

: fix)

X EIR , base B (typically 2), n

fl Cx) = I (O

.lo,be 63 .

- ton)p . Be*I OE bi E p -I ( B

- a 4913

Ht) to,to

(B -- co do, 1,2 , . .,93)

I i sign

A. bide - - ton)p : mantissa

e : exponent( - m seem)

Exe : f- 2 m

Imig = (O .I 00072×2-3=2-4--6.0625),o

Imax = (O

.II 111×23=(111.11--4.5),o

oulyaFINITE.name#of numbers are representable

Not pnnelgtresentddeRepresentabley#"""""""""""MBBBao Xmm Distribution Xmax It Density v

underflow overflow

IEEE754standard-flcxj.TT#EkTYantis Exponent

single precision(32 - bits) (

I,23,8)

double -

'

precision(64- bits) ( I >52,11

)

quadruple -precision(128-bits) ( 1,112,4)