5. Consider the matrix 2-1 A = -1 2. -1 -1 2 Taking A to be a 10 by 10 matrix, try the following: (a) What information does Gerschgorin's theorem give you about the eigenvalues of this matrix? (b) Implement the power method to compute an approximation to the eigenvalue of largest absolute value and its corresponding eigenvector. [Note: Use a random initial vector. If you choose something special, like the vector of all 1s, it may turn out to be orthogonal to the eigenvector you are looking for.] Turn in a listing of your code together with the eigenvalue/eigenvector pair that you computed. Once you have a good approximate eigenvalue, look at the error in previous approximations and comment on the rate of convergence of the power method.

5. Consider the matrix 2-1 A = -1 2. -1 -1 2 Taking A to be a 10 by 10 matrix, try the following: (a) What information does Gerschgorin's theorem give you about the eigenvalues of this matrix? (b) Implement the power method to compute an approximation to the eigenvalue of largest absolute value and its corresponding eigenvector. [Note: Use a random initial vector. If you choose something special, like the vector of all 1s, it may turn out to be orthogonal to the eigenvector you are looking for.] Turn in a listing of your code together with the eigenvalue/eigenvector pair that you computed. Once you have a good approximate eigenvalue, look at the error in previous approximations and comment on the rate of convergence of the power method.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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