Math 430/630 - Matrix Analysis

Fall 2002 - Matthias K. Gobbert

Schedule

This schedule is designed to give you an overview of the material to be covered and is tentative in nature.
The Lecture numbers refer to Lloyd N. Trefethen and David Bau, III, Numerical Linear Algebra, SIAM, 1997 and 2000. Note: SIAM has published both a softcover (1997) and a hardcover (2000) version of this book; they are identical in content.
The Section numbers refer to David S. Watkins, Fundamentals of Matrix Computations, second edition, Wiley, 2002.

Lecture	Date	Main Topic
1	Th 08/29	Matrix-Vector Multiplication	Lecture 1
2	Tu 09/03	Orthogonal Vectors and Matrices	Lecture 2
3, #1	Th 09/05	Vector Norms	Lecture 3
4	Tu 09/10	Matrix Norms	Lecture 3
5, #2	Th 09/12	Matrix Norms	Lecture 3
6	Tu 09/17	Matrix Norms	Lecture 3
7	Th 09/19	The Singular Value Decomposition	Lecture 4
8, #3	Tu 09/24	The Singular Value Decomposition	Lecture 4
9	Th 09/26	More on the Singular Value Decomposition	Lecture 5
10	Tu 10/01	QR via Classical Gram-Schmidt Algorithm	Lecture 7
11, #4	Th 10/03	Householder Triangularization	Lecture 10
12	Tu 10/08	QR via Householder Triangularization	Lecture 10
13	Th 10/10	Least Squares Problems	Lecture 11
14	Tu 10/15	Triangular Linear Systems	Lecture 20
15, #5	Th 10/17	Midterm Exam
16	Tu 10/22	Gaussian Elimination	Lecture 20
17	Th 10/24	Gaussian Elimination with Partial Pivoting	Lecture 21
18	Tu 10/29	Stability of Gaussian Elimination	Lecture 22
19, #6	Th 10/31	Rationale for Iterative Methods	Section 7.1
20	Tu 11/05	Classical Iterative Methods	Section 7.2
21	Th 11/07	Convergence Analysis for Classical Iterative Methods	Section 7.3
22, #7	Tu 11/12	The Method of Steepest Descent	Section 7.4
23	Th 11/14	The Conjugate Gradient Method	Section 7.6
24	Tu 11/19	The Preconditioned Conjugate Gradient Method	Section 7.6
25, #8	Th 11/21	Review of Eigenvalue Theory	Lecture 25
26	Tu 11/26	Numerical Methods for One Eigenvalue	Lecture 27
	Th 11/28	Thanksgiving Holiday
27	Tu 12/03	Numerical Methods for All Eigenvalues	Lecture 26
28, #9	Th 12/05	Numerical Methods for All Eigenvalues	Lecture 28
29	Tu 12/10	Computer numbers: IEEE-standard for floating-point numbers