Prepared by Roland Freund and approved by the campus in Spring 2008.
Course Request Summary
Department Submitting Request: Mathematics
Request for Action: NEW
Effective: 201001
Course Subject Area: Mathematics
Subject Code: MAT
Course Number: 226B
Descriptive Title: Numerical Methods: Large-Scale Matrix Computations
Abbreviated Title: Matrix Computations
Units: 4
Learning Activity
1st LEC 3.0 hrs/wk
2nd T-D 1.0 hrs/wk
In Progress Grading: None
Consent of Instructor: No
Prerequisite(s): 167 or equivalent, or consent of instructor; familiarity with some programming language.
Restrictions on Enrollment: None
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.
General Education: No GE certification
Topical Breadth:
Diversity:
Writing Experience:
Cross Listing:
Justification:
Repeat Credit: No
Credit Limitations: None
Mode of Grading: Letter
Quarters to be Offered: II, Alternate Years
Instructors Name(s): Staff, Chair in Charge
Title(s):
Remarks:
Expanded Course Description
1. SUMMARY OF COURSE CONTENTS:
- 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
2. ILLUSTRATIVE READING:
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
3. FINAL EXAMINATION REQUIREMENT:
Homework assignments, covering both theory and computational problems: 50%.
Final project and report: 50%
4. JUSTIFICATION OF UNITS:
Student workload is 3 hours of lecture, 6 hours of outside preparation, and 3 hours of term paper research and writing for a total of 12 hours per week.
5. POTENTIAL COURSE OVERLAP:
With the cancellation of MAT 229AB, which is being replaced by the new MAT 226ABC series, there is no overlap of this proposed course with any other graduate-level course offered by the Department of Mathematics.
A few topics of this proposed course are also covered in ECS 231 (Large-Scale Scientific Computation), but the focus in ECS 231 is on applications and software related aspects of these topics. The focus of this course, however, is on a rigorous mathematical treatment of these topics. Therefore, the potential overlap of ECS 231 and this proposed course is minimal.
6. GENERAL EDUCATION JUSTIFICATION: None
7. ADDITIONAL INFORMATION FOR STUDENTS: None.