Take the equation f (x) x2 x3 1 Consider the problem of finding the root in 0,1 (a) Start with the Newton method Find the derivative f 0(x) and the iteration rule xi xi1 (b) Starting with x1 1, apply the Newton iteration to find x2 (c) Make a second Newton step to find x3 (d) Now try the bisection ...

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Take the equation f (x) x2 x3 1. Consider the problem of finding the root in

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Take the equation f (x) Æ x2 Åx3 ¡1. Consider the problem of finding the root in [0,1].

(a) Start with the Newton method. Find the derivative f 0(x) and the iteration rule xi !xiÅ1.

(b) Starting with x1 Æ 1, apply the Newton iteration to find x2.

(c) Make a second Newton step to find x3.

(d) Now try the bisection method. Calculate f (0) and f (1). Do they have opposite signs?

(e) Calculate two bisection iterations.

(f ) Compare the Newton and bisection estimates for the root of f (x).

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Probability And Statistics For Economists

ISBN: 9780691235943

1st Edition

Authors: Bruce Hansen

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Question Posted: Sep 23, 2024 07:01 AM

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Take the equation f (x) x2 x3 1. Consider the problem of finding the root in

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Probability And Statistics For Economists

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