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Let A be a given positive constant and g{x) = 2x Ax2 . a. Show that iffixed-point

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 20 Chapter 2.2

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 20

Let A be a given positive constant and g{x) = 2x Ax2 . a. Show that iffixed-point iteration converges to a nonzero limit, then the limit is p = 1 /A, so the inverse of a number can be found using only multiplications and subtractions. b. Find an interval about 1/A for which fixed-point iteration converges, provided po is in that interval

Step-by-Step Solution:
Step 1 of 3

a lvt,+t-// w q/zzla ''{3r^Jr^S*,ts,Qr-^ a" n' n qG'wifr*'b^o i1 :/=q/f;o P= ','tso; !30:2q,+ 3' t 2Z-no ;o, ','G,+,o)(o-s){o fl=-to ffil Tlr f= 2. tltPt lx il-swx'+sx- @ s)0rD_ I PJ lin i X+s 3 o ffi_s ',, / A- 3, Naqr'{xx-7- o x-q t[wsr3 -€-"-->f il v76:r3' -@ : iltn t = -l ffrtsl x+4 tlTrsts 3t3 a ,U le llin XZ_ 7 0 drr;&r9 W->s-YL 6x+q o

Step 2 of 3

Chapter 2.2, Problem 20 is Solved
Step 3 of 3

Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Let A be a given positive constant and g{x) = 2x Ax2 . a. Show that iffixed-point