Peter Blomgren
San Diego State University
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Math 543: Numerical Matrix Analysis Spring 2014
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Notes and Resources...

are linked from the schedule.

Catalog description

Gaussian elimination, LU-factorizations and pivoting strategies. Direct and iterative methods for linear systems. Iterative methods for diagonalization and eigensystem computation. Tridiagonal, Hessenberg, and Householder matrices. The QR algorithm.

Prerequisites
  • 1. Math 541 (Introduction to Numerical Analysis and Computing)
  • 2. Math 254 (Introduction to Linear Algebra), or
  • 2. Math 342A (Methods of Applied Mathematics)

Computational Resources:

You must have access to the current release of Matlab. Class accounts for the labs will be available. You can also use SDSU's Rohan Sun Enterprise system or another capable system. [How to open a ROHAN account].

Students with Disabilities:

If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact Student Disability Services at (619)594-6473. To avoid any delay, please contact Student Disability Services as soon as possible. Please note that accommodations are not retroactive, and cannot be provided until an accommodation letter from Student Disability Services is received by the Professor.

Required Text and Reading Materials:

Numerical Linear Algebra, Lloyd N. Trefethen and David Bau, III, Society for Industrial and Applied Mathematics (SIAM), 1997. ISBN 0-89871-361-7. Note: SIAM Student Membership is (still, hopefully) FREE, which means you can get the member price!

Class web page [http://terminus.sdsu.edu/SDSU/Math543_s2014/], and handouts.

Course Outline (as of 1/20/2014):

Trefethen/Bau: I-Fundamentals: Matrix-VEctor Multiplication, Orthogonal Vectors and Matrices, Norms, The Singular Value Decomposition, More on the SVD. II-QR Factorization and Least Squares: Projectors, QR Factorization, Gram-Schmidt Orthogonalization, Householder Triangularization, Least Squares Problems. III-Conditioning and Stability: Conditioning and Condition Numbers, Floating Point Arithmetic, Stability, Stability of Householder Triangularization and Back Substitution, Conditioning of Least Squares Problems, Stability of Least Squares Algorithms. IV-System of Equations: Gaussian Elimination, Pivoting, Stability of Gaussian Elimination, Cholesky Factorization. V-Eigenvalues Eigenvalue Problems and Algorithms, Reduction to Hessenberg and Tridiagonal Form, Rayleigh Quotient, Inverse Iteration, QR Algorithm without and with Shifts, Computing the SVD. VI-Iterative Methods: Overview, Arnoldi Iteration, GMRES, ((Lanczos Iteration)), ((From Lanzcos to Gauss Quadrature)), ((Conjugate Gradients)), ((Biorthogonalization Methods)), ((Preconditioning)).

Professor

Peter Blomgren
blomgren DOT peter AT gmail DOT com
Class hours: TuTh 4:00p – 5:15a, GMCS-328
Office hours: TuTh 2:00p – 3:30p, and by appointment, GMCS-587.

Copyright © 2014 Peter Blomgren.