TOPICS IN NUMERICAL LINEAR ALGEBRA

Credit Hours: 1-3 · Graduate

Selected topics will vary depending on instructor and student interests. Derivation and analysis of Krylov and subspace iteration methods for large eigenvalue problems (Lanczos, Arnoldi, Jacobi-Davidson algorithms); preconditioning for linear systems and eigenvalue problems (incomplete LU, domain decomposition, multigrid); convergence analysis including potential theory and pseudospectra. Applications: regularization of discrete inverse problems; dimension reduction for large dynamical control systems; effects on non-normality on behavior of dynamical systems and iterative processes. Instructor Permission Required. Recommended Prerequisite(s): CAAM 551 or CMOR 525 Repeatable for Credit.