Winter 2007 Math 510
What, When, and Where:
Course Description:
Numerical Methods for Linear Algebra: Numerical matrix algebra, orthogonalization and least squares methods, eigenvalue problems, iterative methods, applications.
Text:
Lectures:
TuTh 9:30a - 10:45a F454 HFAC (Fine Arts Building)
Office Hours:
T 05:00-05:50
H 01:30-02:30
Grading Scheme:
20% Exam #1
20% Exam #2
20% Exam #3
40% Homework
Course Schedule: (subject to change)
Jan 09 Vector spaces, subspaces, spans, linear combinations
Jan 11 Linear independence, basis, dimensions, direct sums
Jan 16 Linear transformations, matrix representations, similarity
Jan 18 Elem. matrices, fund. subspaces, rank-nullity, LU decomp.
Jan 23 Inner prod spaces, orthonormal sets, Gram Schmidt, QR decomp.
Jan 25 Ortho comp., adjoints, fund. subspaces, projectors, least squares
Jan 30 E-values, e-vectors, simple & semisimple operators
Feb 01 Normal operators, spectral theorem, Cholesky decomposition
Feb 06 Positive definite operators, quadratic forms, gen. e-vectors
Feb 08 SVD & applications
Feb 13 Finite-precision arithmetic and computation
Feb 15 Conditioning
Feb 22 Stability
Feb 27 LU decomposition with pivoting
Mar 01 Exam I
Mar 06 Modified Gram Schmidt, Householder triangularization
Mar 08 Least squares, power method
Mar 13 Reduction to Hessenberg or tridiagonal form
Mar 15 Rayleigh quotients, inverse iterations
Mar 20 QR method with and without shifts
Mar 22 Other methods and the SVD
Mar 27 Overview of iterative methods
Mar 29 Arnoldi iteration
Apr 03 GMRES
Apr 05 Lanczos iteration
Apr 10 Conjugate gradient method
Apr 12 Bi-orthogonalization methods
Apr 17 Preconditioning
Assignments:
Assignment #1 (Due 01/23/07)
All problems in Chapter #1 of notes (not Trefethen).
Assignment #2 and #3 (Due 02/06/07)
All problems in Chapter #2 and #4 of notes (not Trefethen).
Assignment #4 (Due 02/27/07)
All problems in Chapter #6 of notes (not Trefethen).
Assignment #5 (Due 03/15/07)
Labs handed out in class.