Evangelos A. Coutsias, Math 464

Math 504/CS 575: Numerical Linear Algebra

10484 - 001 --- T Th 11:00-12:15 ASM. 1068

Instructor: Evangelos A. Coutsias

Required Text 1: L.N. Trefethen and D. Bau Numerical Linear Algebra

Required Text 2: J. W. Demmel Applied Numerical Linear Algebra

Computing Projects

  • Term Project
  • Term Project Data
  • On the starting vector (from Wilkinson)
    The Rayleigh quotient iteration and its convergence:
  • Iterative relaxation procedures for eigenvalue problems, S.H. Crandall, Proc. Royal Soc. 207, 416-423, 1951.
  • On the convergence of the rayleigh quotient iteration for the computation of the characteristic roots and vectors. II A. M. Ostrowski Arch. Rational Mech. Anal. I: 1, 233-241, 1958 and II: 2(1), 423-428, 1958.
    Extensions
  • The Rayleigh quotient and some of its generalizations for nonormal matrices B.N. Parlett, Math. Comp. 28(127), 679-693, 1974.
  • Rayleigh Quotient Iteration for Nonsymmetric Matrices S. Batterson & J. Smillie, Mathematics of Computation, Vol. 55, No. 191 (Jul., 1990), pp. 169-178.
  • Email Hotline

    The computing projects should be done using MATLAB.
    Some good reference sites are Numerical Methods , and Netlib . Arnoldi Package .
    Some helpful matlab commands and functions are summarized in
    Chapter 1 while the linear algebra commands are summarized in
    Chapter 9 of the text "MATLAB Guide" by Higham and Higham (SIAM, 2000).
    strass.m script for Strassen multiplication of matrices
    psa.m script for computing Pseudospectra
    radke.ps.gz Radke's thesis on implementing Arnoldi in Matlab (gzip)

    Outline

    Homework Problems

    Return to: Department of Mathematics and Statistics, University of New Mexico.

    <vageli aT math.unm.edu>
    Last updated: March 08, 2000