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(3) Consider the matrix 3 01 A = 0 32 1 2 3 (a) By using the Gerschgorin theorem, verify that all the eigenvalues for A are all positive.

(3) Consider the matrix 3 01 A = 0 32 1 2 3 (a) By using the Gerschgorin theorem, verify that all the eigenvalues for A are all positive.

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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(3) Consider the matrix 3 0 1 A = 0 3 2 1 2 3 (a) By using the Gerschgorin theorem, verify that all the eigenvalues for A are all positive. (b) Use power method to compute the dominant eigenvalue, A1 of A and its associated eigenvector v1. Use v0) = (0,0, 1)" and stop the iteration when |mk+1 – mk| < 0.0005. Do your calculation in four decimal places (4DP). (c) By using shifted power method with shifting factorp= 11, compute the smallest eigen- value, A3 and its corresponding eigenvector, v3. v0) = (0,0, 1)" and stop the iteration when ||a* – x(k-'ll < 0.0005. Do your calculation in four decimal places (4DP). (d) Using results obtained from part (a) and (b), find the other eigenvalue, A2 of A.
Transcribed Image Text:(3) Consider the matrix 3 0 1 A = 0 3 2 1 2 3 (a) By using the Gerschgorin theorem, verify that all the eigenvalues for A are all positive. (b) Use power method to compute the dominant eigenvalue, A1 of A and its associated eigenvector v1. Use v0) = (0,0, 1)" and stop the iteration when |mk+1 – mk| < 0.0005. Do your calculation in four decimal places (4DP). (c) By using shifted power method with shifting factorp= 11, compute the smallest eigen- value, A3 and its corresponding eigenvector, v3. v0) = (0,0, 1)" and stop the iteration when ||a* – x(k-'ll < 0.0005. Do your calculation in four decimal places (4DP). (d) Using results obtained from part (a) and (b), find the other eigenvalue, A2 of A.
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