MA 522 - Matrix Theory and Numerical Linear Algebra I.

Review of basic linear algebra from a constructive and geometric point of view. Factorizations of Gauss, Cholesky and Gram-Schmidt; determinants; linear least squares problems; rounding error analysis; stable methods for updating matrix factorizations and for linear programming; introduction to Hermitian eigenvalue problems and the singular value decomposition via the QR algorithm and the Lanczos process; method of conjugate gradients. (Same as CS 522.)

Prerequisite: MA 322.

Status of Course: Course functioning each fall.

MA 537 - Numerical Analysis.

Finite-precision (floating-point) arithmetic; solution of non-linear equations; approximation of functions; numerical differentiation and integration; numerical solution of ordinary differential equations. (Same as CS 537 and EGR 537.)

Prerequisite: MA 322.

Status of Course: Course functioning.

MA 622 - Matrix Theory and Numerical Linear Algebra II.

Numerical solution of matrix eigenvalue problems and applications of eigenvalues; normal forms of Jordan and Schur; vector and matrix norms; perturbation theory and bounds for eigenvalues; stable matrices and Lyapunov theorems; nonnegative matrices; iterative methods for solving large sparse linear systems.

Prerequisite: MA 522 or consent of instructor.

MA 721 - Selected Topics in Numerical Analysis.

Review of current research in numerical analysis. May be repeated to a maximum of nine credits.

Prerequisite: Consent of instructor.

MA 777 - Mathematical Seminar.

May be repeated once for a total of six credits..

Prerequisite: Consent of instructor.