MATH 6664-001 and C SC 5646-001: Numerical Linear Algebra
Spring 1996. University of Colorado Denver

HOURS: MW 6:55-8:10 pm (WC 235)

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm
WWW: http://math.ucdenver.edu/~aknyazev

TEXTBOOK:
Iterative Solution Methos. Owe Axelsson. Cambridge University Press, 1994.

SUBJECT:
Solution of linear equations, eigenvector and eigenvalue calculations, matrix error analysis, iterative methods.

The course will require knowledge in linear algebra, a basic knowledge of numerical methods, some programming experience, and familiarity with the complex plane. A brief review will be presented if necessary. The class will involve MATLAB workshops and some programming assingments in the MATLAB language.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

• 1. Direct solution methods
• 2. Theory of matrix eigenvalues
• 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems
• 5. Basic iterative methods and their rates of convergence
• 10. Estimates of eigenvalues and condition numbers for preconditioned matrices
• 11. Conjugate gradient and Lanczos-Type methods
• 12. Generalized conjugate gradient methods
• 13. The rate of convergence of the conjugate gradient method