(a) Use 4 iterations of the power method to calculate an estimate of the maximal mag- nitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1) as the initial estimate of the eigenvector. Given that the the inverse of matrix A is A-¹. 1 144 16 6 10 8 12 -4 6 -9 33 (b) Use this matrix to perform 3 iterations of the power method to calculate an estimate of the minimal magnitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1) as the initial estimate of the eigenvector.

(a) Use 4 iterations of the power method to calculate an estimate of the maximal mag- nitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1) as the initial estimate of the eigenvector. Given that the the inverse of matrix A is A-¹. 1 144 16 6 10 8 12 -4 6 -9 33 (b) Use this matrix to perform 3 iterations of the power method to calculate an estimate of the minimal magnitude eigenvalue of A and an estimate of the corresponding eigenvector. Start with (1,1,1) as the initial estimate of the eigenvector.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.5: Iterative Methods For Computing Eigenvalues

Problem 15EQ

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