4.3. (a) Implement inverse iteration with a shiftto compute the eigenvalue nearest to 2, and a cor-responding normalized eigenvector, of the matrix[6 2 1A = 2 3 11 11You may use an arbitrary starting vector.(b) Use a real symmetric eigensystem library rou-tine to compute all of the eigenvalues and eigen-vectors of the matrix, and compare the resultswith those obtained in part a.

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4.3. (a) Implement inverse iteration with a shift to compute the eigenvalue nearest to 2, and a cor- responding normalized eigenvector, of the matrix [6 2 11 A = 2 3 1 1 1 1 You may use an arbitrary starting vector.

4.3. (a) Implement inverse iteration with a shift to compute the eigenvalue nearest to 2, and a cor- responding normalized eigenvector, of the matrix [6 2 11 A = 2 3 1 1 1 1 You may use an arbitrary starting vector.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

4.3. (a) Implement inverse iteration with a shift
to compute the eigenvalue nearest to 2, and a cor-
responding normalized eigenvector, of the matrix
[6 2 1
A = 2 3 1
1 1
1
You may use an arbitrary starting vector.
(b) Use a real symmetric eigensystem library rou-
tine to compute all of the eigenvalues and eigen-
vectors of the matrix, and compare the results
with those obtained in part a.

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