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Unformatted text preview: Homework 10  Due Wed. Nov. 16th
Math 224  Fall 2011
Dr. Mauro Maggioni
Oﬃce hours: Tue 45, in oﬃce 293 Physics Bldg.
Phone: 6602825
Web page: www.math.duke.edu/˜ mauro
Email: 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
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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.
 Fall '08
 Layton,A
 Math

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