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Get Full Access to Numerical Analysis - 10 Edition - Chapter 9.3 - Problem 24
Get Full Access to Numerical Analysis - 10 Edition - Chapter 9.3 - Problem 24

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# Annihilation Technique Suppose the n y. n matrix A has eigenvalues A.|,... , Xn ordered ISBN: 9781305253667 457

## Solution for problem 24 Chapter 9.3

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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##### ISBN: 9781305253667

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