Course Schedule and Catalog

Long Title: NUMERICAL LINEAR ALGEBRA

Department: *Computational & Applied Math*

Grade Mode: Standard Letter

Language of Instruction: Taught in English

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): CAAM 453 OR CAAM 553 OR CAAM 550

Description: Direct methods for large, sparse linear systems; regularization of ill-conditioned least squares problems; backward error analysis of basic algorithms for linear equations and least squares, sensitivity and conditioning of linear systems and least square problems; condition estimation. Preconditioned iterative methods for linear systems (CG, GMRES, BiCGstab, QMR); multigrid methods. Matrix theory including spectral decompositions, Schur form, eigenvalue perturbation theory, and the geometry of subspaces. Eigenvalue algorithms, Sylvester and Lyapunov equations, the implicitly shifted QR algorithm, computation of the SVD, generalized eigenvalue problems. Introduction to large scale eigenvalue algorithms. Proficiency in MATLAB and acquaintance with one or more of C, F77, C++, F90 is required. Recommended Prerequisite(s) CAAM 453 or CAAM 553 or CAAM 550