10th Edition

ISBN: 9781305253667

Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden

Publisher: Cengage Learning

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Textbook Question

Chapter 2.2, Problem 26ES

Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p of g. Show that if |g′(p)| < 1, then there exists a δ > 0 such that if |p₀ − p| ≤ δ, then the fixed-point iteration converges.

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Chapter 2.2, Problem 25ES

Chapter 2.2, Problem 1DQ

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Chapter 2 Solutions

Numerical Analysis

Ch. 2.1 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.1 - Let f(x) = 3(x +1)(x 12)(x 1) = 0. Use the...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Use the Bisection method to find solutions...Ch. 2.1 - Prob. 7ES Ch. 2.1 - Prob. 8ES Ch. 2.1 - Prob. 9ES Ch. 2.1 - Prob. 10ES Ch. 2.1 - Prob. 11ES

Ch. 2.1 - Let f(x) = (x + 2)(x + 1)x(x 1)3(x 2). To which...Ch. 2.1 - Find an approximation to 253 correct to within 104...Ch. 2.1 - Find an approximation to 3 correct to within 104...Ch. 2.1 - A trough of length L has a cross section in the...Ch. 2.1 - Use Theorem 2.1 to find a bound for the number of...Ch. 2.1 - Prob. 18ES Ch. 2.1 - Prob. 19ES Ch. 2.1 - Let f(x) = (x 1)10, p = 1, and pn = 1 + 1/n. Show...Ch. 2.1 - The function defined by f(x) = sin x has zeros at...Ch. 2.1 - Prob. 1DQ Ch. 2.1 - Prob. 2DQ Ch. 2.1 - Is the Bisection method sensitive to the starting...Ch. 2.2 - Use algebraic manipulation to show that each of...Ch. 2.2 - a. Perform four iterations, if possible, on each...Ch. 2.2 - Let f(x) = x3 2x + 1. To solve f(x) = 0, the...Ch. 2.2 - Let f(x) = x4 + 3x2 2. To solve f(x) = 0, the...Ch. 2.2 - The following four methods are proposed to compute...Ch. 2.2 - Prob. 6ES Ch. 2.2 - Prob. 7ES Ch. 2.2 - Prob. 8ES Ch. 2.2 - Use Theorem 2.3 to show that g(x) = + 0.5...Ch. 2.2 - Use Theorem 2.3 to show that g(x) = 2x has a...Ch. 2.2 - Use a fixed-point iteration method to find an...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Prob. 20ES Ch. 2.2 - Prob. 21ES Ch. 2.2 - a. Show that Theorem 2.3 is true if the inequality...Ch. 2.2 - a. Use Theorem 2.4 to show that the sequence...Ch. 2.2 - Prob. 24ES Ch. 2.2 - Prob. 25ES Ch. 2.2 - Suppose that g is continuously differentiable on...Ch. 2.3 - Let f(x) = x2 6 and p0 = 1. Use Newtons method to...Ch. 2.3 - Let f(x) = x3 cos x and p0 = 1. Use Newtons...Ch. 2.3 - Let f(x) = x2 6. With p0 = 3 and p1 = 2, find p3....Ch. 2.3 - Let f(x) = x3 cos x. With p0 = 1 and p1 = 0, find...Ch. 2.3 - Prob. 11ES Ch. 2.3 - Prob. 12ES Ch. 2.3 - The fourth-degree polynomial...Ch. 2.3 - Prob. 14ES Ch. 2.3 - Prob. 15ES Ch. 2.3 - Prob. 16ES Ch. 2.3 - Prob. 22ES Ch. 2.3 - Prob. 23ES Ch. 2.3 - Prob. 24ES Ch. 2.3 - Prob. 25ES Ch. 2.3 - Prob. 27ES Ch. 2.3 - A drug administered to a patient produces a...Ch. 2.3 - Prob. 30ES Ch. 2.3 - Prob. 32ES Ch. 2.3 - Prob. 1DQ Ch. 2.3 - Prob. 2DQ Ch. 2.3 - Prob. 3DQ Ch. 2.3 - Prob. 4DQ Ch. 2.4 - Prob. 6ES Ch. 2.4 - a. Show that for any positive integer k, the...Ch. 2.4 - Prob. 8ES Ch. 2.4 - a. Construct a sequence that converges to 0 of...Ch. 2.4 - Prob. 10ES Ch. 2.4 - Prob. 11ES Ch. 2.4 - Prob. 12ES Ch. 2.4 - Prob. 13ES Ch. 2.4 - Prob. 14ES Ch. 2.4 - Prob. 1DQ Ch. 2.4 - Prob. 2DQ Ch. 2.4 - Prob. 4DQ Ch. 2.5 - Let g(x) = cos(x 1) and p0(0) = 2. Use...Ch. 2.5 - Prob. 4ES Ch. 2.5 - Prob. 5ES Ch. 2.5 - Prob. 6ES Ch. 2.5 - Use Steffensens method to find, to an accuracy of...Ch. 2.5 - Prob. 8ES Ch. 2.5 - Prob. 9ES Ch. 2.5 - Use Steffensens method with p0 = 3 to compute an...Ch. 2.5 - Use Steffensens method to approximate the...Ch. 2.5 - Prob. 12ES Ch. 2.5 - Prob. 13ES Ch. 2.5 - Prob. 14ES

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Suppose that g is continuously differentiable on some interval ( c , d ) that contains the fixed point p of g . Show that if | g ′( p )| < 1, then there exists a δ > 0 such that if | p 0 − p | ≤ δ , then the fixed-point iteration converges.

Solution Summary: The author explains that if g(p)=p, then the fixed-point iteration converges.

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Chapter 2 Solutions

Suppose that g is continuously differentiable on some interval ( c , d ) that contains the fixed point p of g . Show that if | g ′( p )| &lt; 1, then there exists a δ &gt; 0 such that if | p 0 − p | ≤ δ , then the fixed-point iteration converges.

Solution Summary: The author explains that if g(p)=p, then the fixed-point iteration converges.

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Chapter 2 Solutions

Suppose that g is continuously differentiable on some interval ( c , d ) that contains the fixed point p of g . Show that if | g ′( p )| < 1, then there exists a δ > 0 such that if | p 0 − p | ≤ δ , then the fixed-point iteration converges.