Advanced Numerical Linear Algebra
''Advanced topics in numerical linear algebra including pseudo-spectra, rounding error analysis and perturbation theory, numerical methods for problems with special structure, and numerical methods for large scale problems.
Iterative Methods for Sparse Linear Systems, 2nd edition, Saad, SIAM, 2003.
Basic iterative methods for linear systems and linear eigenvalue problems; deflation techniques; general projection methods; Krylov subspace methods; pre-conditioning; multigrain methods; domain decomposition methods; perturbation theory and error analysis; non-standard eigenvalue problems.
Students should be comfortable with concepts from linear algebra (Math 590 and (or) Math 591) and numerical analysis (Math 781 and 782), e.g. Gaussian elimination; LU, Cholesky and QR factorization; QR algorithm. Programming assignments will be an essential part of the course. If you have any questions about the course prerequisites, please contact the instructor.
(Xu 2018 )