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. Possible Instructors: Ding, Ye. 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 MA 537 and EGR 537.)Prerequisite: MA 322. Possible Instructors: Ding, Qin, Ye. 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. |
