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1. One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. (15pts) Consider the matrix 02024, 5:21:12 PM 10-20 A = -2 0 -2 5 +4 -2 (a) Perform 3 iterations of the Power method to estimate the largest eigenvalue. Begin with an initial guess of o = [1,0,0] and use infinity norm (largest absolute value) as the eigenvalue and normalization factor. (12pts) (b) Use (c) Compute the fg to compute the smallest eigenvalue. (1pts) e ratio of your estimate of the largest and the smallest eigenvalues. Compare the results with MATLAB's values for cond. (2pts)

1. One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. (15pts) Consider the matrix 02024, 5:21:12 PM 10-20 A = -2 0 -2 5 +4 -2 (a) Perform 3 iterations of the Power method to estimate the largest eigenvalue. Begin with an initial guess of o = [1,0,0] and use infinity norm (largest absolute value) as the eigenvalue and normalization factor. (12pts) (b) Use (c) Compute the fg to compute the smallest eigenvalue. (1pts) e ratio of your estimate of the largest and the smallest eigenvalues. Compare the results with MATLAB's values for cond. (2pts)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
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1. One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. (15pts) Consider the matrix 02024, 5:21:12 PM 10-20 A = -2 0 -2 5 +4 -2 (a) Perform 3 iterations of the Power method to estimate the largest eigenvalue. Begin with an initial guess of o = [1,0,0] and use infinity norm (largest absolute value) as the eigenvalue and normalization factor. (12pts) (b) Use (c) Compute the fg to compute the smallest eigenvalue. (1pts) e ratio of your estimate of the largest and the smallest eigenvalues. Compare the results with MATLAB's values for cond. (2pts)
Transcribed Image Text:1. One estimate that can be used for the condition number of a matrix is the ratio of the largest and smallest eigenvalues. In fact, for real symmetric matrices, that turns out to be exactly the condition number. (15pts) Consider the matrix 02024, 5:21:12 PM 10-20 A = -2 0 -2 5 +4 -2 (a) Perform 3 iterations of the Power method to estimate the largest eigenvalue. Begin with an initial guess of o = [1,0,0] and use infinity norm (largest absolute value) as the eigenvalue and normalization factor. (12pts) (b) Use (c) Compute the fg to compute the smallest eigenvalue. (1pts) e ratio of your estimate of the largest and the smallest eigenvalues. Compare the results with MATLAB's values for cond. (2pts)
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