Let F : R → R be given by F(x) = (x – c)*, where x € R is a constant. Suppose that we apply Newton's method to the problem of minimizing F. Let y = |x* - c], where x is the kth iteration in Newton's method. Show that the %3D sequence {y*} satisfies y*+1 = . Show that x* → c for any initial guess.
Let F : R → R be given by F(x) = (x – c)*, where x € R is a constant. Suppose that we apply Newton's method to the problem of minimizing F. Let y = |x* - c], where x is the kth iteration in Newton's method. Show that the %3D sequence {y*} satisfies y*+1 = . Show that x* → c for any initial guess.
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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Solve the question (picture 1) with the "NEWTON FORMULA" in picture2.
Transcribed Image Text:2. Let F : R → R be given by F(x) = (x – c)*, where x e R is a constant. Suppose that we
apply Newton's method to the problem of minimizing F.
Let y = |x* - cl, where x is the kth iteration in Newton's method. Show that the
sequence {y*} satisfies y*+! :
Show that x*
→ c for any initial guess.
Transcribed Image Text:Ck)
(K)
-F(x ) )
%3D
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