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Choose o = [1,0,0]. Compute an approximation for the eigenvalue of A with largest absolute value Xamax(A) and the corresponding eigenvector by using power iteration. Plot the error Xamax (A) - μ| as a function of the index i = 0, 1,..., 10.

Choose o = [1,0,0]. Compute an approximation for the eigenvalue of A with largest absolute value Xamax(A) and the corresponding eigenvector by using power iteration. Plot the error Xamax (A) - μ| as a function of the index i = 0, 1,..., 10.

Advanced Engineering Mathematics
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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4. The eigenvalues of a matrix A € Cnxn are usually not computed in practice by finding the zeros of the characteristic polynomial. One way to approximate the eigenvector corre- sponding to the eigenvalue of a diagonalizable matrix A with largest absolute value is power iteration, Axi ||Axi||2 Xi+1 i = 0, 1, 2, ..., where o C is some initial guess. Approximation for the eigenvalue of A with largest absolute value is computed as Hi = R(A, x₂), i = 0, 1, 2, ... (1) The intuition behind power iteration is that repeated multiplication by A turns the vector slowly towards the eigenvector corresponding to the eigenvalue of A with largest absolute value (unless xo is orthogonal to it). Let now [2 1 0] A = 1 2 1 0 1 2 Choose o [1,0,0]¹. Compute an approximation for the eigenvalue of A with largest absolute value Xamax (A) and the corresponding eigenvector by using power iteration. Plot the error Xamax (A) — μ| as a function of the index i = 0, 1,..., 10.
Transcribed Image Text:4. The eigenvalues of a matrix A € Cnxn are usually not computed in practice by finding the zeros of the characteristic polynomial. One way to approximate the eigenvector corre- sponding to the eigenvalue of a diagonalizable matrix A with largest absolute value is power iteration, Axi ||Axi||2 Xi+1 i = 0, 1, 2, ..., where o C is some initial guess. Approximation for the eigenvalue of A with largest absolute value is computed as Hi = R(A, x₂), i = 0, 1, 2, ... (1) The intuition behind power iteration is that repeated multiplication by A turns the vector slowly towards the eigenvector corresponding to the eigenvalue of A with largest absolute value (unless xo is orthogonal to it). Let now [2 1 0] A = 1 2 1 0 1 2 Choose o [1,0,0]¹. Compute an approximation for the eigenvalue of A with largest absolute value Xamax (A) and the corresponding eigenvector by using power iteration. Plot the error Xamax (A) — μ| as a function of the index i = 0, 1,..., 10.
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