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Annihilation Technique Suppose the n y. n matrix A has eigenvalues A.|,... , Xn ordered

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 24 Chapter 9.3

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 24

Annihilation Technique Suppose the n y. n matrix A has eigenvalues A.|,... , Xn ordered by |Xi| > |A.21 > IA.3I > > |A.,,I, linearly independent eigenvectors v*", v (2',... , v*"'. Show that ifthe Power method is applied with an initial vector x (0) given by x (0) = /32V(2)+/g3V(3, + ... + /?nV()! then the sequence {/x'"1 '} described in Algorithm 9.1 will converge to A.2. b. Show that for any vector x = ]C/=i the vector x <0) (A k|/)x satisfies the property given in part (a). c. Obtain an approximation to A.2 for the matrices in Exercise 1. d. Show that this method can be continued to find A.3 using x'01 (A A,2/)(A A.| /)x

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Chapter 9.3, Problem 24 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Annihilation Technique Suppose the n y. n matrix A has eigenvalues A.|,... , Xn ordered