Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
- Direct Methods for the Solution of Linear Systems o Sparse Cholesky factorization o Sparse LU factorization o Fast elliptic solvers - Iterative Methods for the Solution of Linear Systems o Krylov subspace methods for symmetric systems o Krylov subspace methods for nonsymmetric systems o Preconditioning o Multigrid methods - Eigenvalue and Singular Value Problems o The power method o Krylov subspace methods o Applications in information retrieval o Applications in image processing - Solution of Least-Squares Problems o Sparse QR factorization - Matrix Compression of Low-Rank Matrices o Randomized algorithms o FMM/HSS algorithm - Linear Programming o Simplex method o Interior-point methods
- G.H. Golub and C.F.Van Loan, Matrix Computations, 3rd Ed., Johns Hopkins University Press, 1996
- Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, 2003
- T.A. Davis, Direct Methods for Sparse Linear Systems, SIAM, 2006