## 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.

MAT 226B: Numerical Methods: Large-Scale Matrix Computations

**Approved:**2008-06-01, Roland Freund

**Units/Lecture:**

Winter, alt years; 1st LEC 3.0 hrs/wk; 2nd T-D 1.0 hrs/wk

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

167 or equivalent, or consent of instructor; familiarity with some programming language.

**Course Description:**

Numerical methods for large-scale matrix computations, including direct and iterative methods for the solution of linear systems, the computation of eigenvalues and singular values, the solution of least-squares problems, matrix compression, methods for the solution of linear programs.

**Suggested Schedule:**

- 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

**Additional Notes:**

No required textbook. Optional references:

- 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

**Assessment:**

Homework assignments, covering both theory and computational problems: 50%.
Final project and report: 50%