Homework_10

Homework_10 - Homework 10 - Due Wed. Nov. 16th Math 224 -...

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Unformatted text preview: Homework 10 - Due Wed. Nov. 16th Math 224 - Fall 2011 Dr. Mauro Maggioni Office hours: Tue 4-5, in office 293 Physics Bldg. Phone: 660-2825 Web page: www.math.duke.edu/˜ mauro E-mail: mauro.maggioni at duke.edu Homework policies: as in homework 1. All the materials (code, figures, etc...) have to be turned in (as printouts!) with your homework, or the homework will not be graded. Assignment Study Lectures 26,27,28 in the book. Exercises 27.5,28.2 (skip the part on Givens rotations), 28.3. The following are parts of exercises from Heath’s Scientific Computing: • List three conditions under which power iteration may fail. • In power iteration or inverse power iteration, why are the vector iterates normalized at each iteration? • Given a symmetric matrix A, which method would you use to compute the following? – The smallest eigenvalue of A. – The largest eigenvalue of A. – The eigenvalue of A closest to some specified scalar β . – All of the eigenvalues of A. • Write a program implementing Rayleigh quotient iteration for computing an eigenvalue and corre 621 sponding eigenvector of a matrix. Test your program on A = 2 3 1 to find the eigenvalue 111 nearest to 2, with a random starting vector. ...
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This note was uploaded on 01/16/2012 for the course MATH 224 taught by Professor Layton,a during the Fall '08 term at Duke.

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