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If a f: R R is unimodal, continuous function on an interval I of length L, how many iterations k of the golden method are needed to estimate the minimizer x* over I with an absolute error of at most 10-m? How large must k be if L = 2 and m = 4?

If a f: R R is unimodal, continuous function on an interval I of length L, how many iterations k of the golden method are needed to estimate the minimizer x* over I with an absolute error of at most 10-m? How large must k be if L = 2 and m = 4?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Golden section unimodal function
If a f: R→ R is unimodal, continuous function on an interval I of length L, how many iterations k of the golden method are needed to estimate the minimizer x* over I with an absolute error of at most 10-m? How large must k be if L = 2 and m = 4? 2 akt, say, then lak - bk|= C for some C> 0 where Solve C ≤ 10-m for k. = Hint: If you take x*~ Pk is p = (1 + √5)/2 (Why?).
Transcribed Image Text:If a f: R→ R is unimodal, continuous function on an interval I of length L, how many iterations k of the golden method are needed to estimate the minimizer x* over I with an absolute error of at most 10-m? How large must k be if L = 2 and m = 4? 2 akt, say, then lak - bk|= C for some C> 0 where Solve C ≤ 10-m for k. = Hint: If you take x*~ Pk is p = (1 + √5)/2 (Why?).
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