Evangelos A. Coutsias, Math 464

Math 504/CS 575: Numerical Linear Algebra

001 --- T Th 8:00-9:15 HUM. 424

Instructor: Evangelos A. Coutsias

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

Recommended Text: J. W. Demmel Applied Numerical Linear Algebra


Computing Projects

  • Term Project
  • 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.
  • The Rayleigh quotient iteration for Generalized Companion Matrix Pencils A. Amiraslani, D.A. Aruliah and R.M. Corless ( 2007 preprint).
  • 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
    house.m script for Householder QR
    mgs.m script for Modified Gram-Schmidt QR
    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: December 26, 2008