MA 692, Sparse and Structured Matrix Computations, Fall 2013

Lectures:TTh 3:00-4:15pm, UNIV 319Instructor: Prof. Jianlin Xia Email:Office: MATH 442 Office Hours: TTh 4:20-5:20pm, and by appointment Course webpage:http://www.math.purdue.edu/~xiaj/teaching/692.13f/

- Lecture notes and references
(subject to change)
- Week 11-12: Structured sparse direct solvers
- Week 9-10: Rank structures and
hierarchically semiseparable matrices (last updated: 10/22)
- A Matlab code for RRQR
- Slides by S. Borm
- Notes by S. Borm., L. Grasedyck, and W. Hackbusch
- References on randomized HSS methods: paper1, paper2

- Week 6-8: Fast multipole method
- Beatson, Greengard, A short course on fast multipole methods

- Week 5-6: Explicitly structured matrices
- Week 3-4: Sparse direct solvers
(last updated: 9/17)
- Jim Demmel's lecture notes on graph partitioning

- Week 1-2:
Introduction (last updated: 8/27)
- A Matlab code to demonstrate catastrophic cancellation
- A Matlab code (by M. Gu) for both an unstable and a stable way for computing the roots of a quadratic polynomial
- A Matlab code for estimating f'(x)
- A Matlab code for three ways to compute the Householder matrix (unstable, stable, stable+)
- A Matlab code for Householder QR
- Matlab codes for classical Gram-Schmidt and modified Gram-Schmidt (by M. Gu), and the test code
- A Matlab code (two examples) showing that the SMW formula is unstable

- Contents

- Course information and resources
- Course outline
(subject to change)
- Introduction
- Sparse direct solvers
- Explicitly structured matrices
- Fast multipole and multilevel summation methods
- Data-sparse and rank structured matrices
- Structured sparse direct solvers
- Randomized direct solvers
- Structured eigenvalue solutions
- Other topics

- Useful seminar series: CAM, CAM lunch, CSE, CS, Math, Science, ECE
- Demmel's lectures notes for Applied Numerical Linear Algebra
- Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide

- Course outline
(subject to change)
**Reference books**- Demmel, Applied Numerical Linear Algebra, 1997
- Golub and Van Loan, Matrix Computations,
**4th ed.**, 2012 - Laub, Computational Matrix Analysis, 2012
- Saad, Iterative Methods for Sparse Linear Systems, 2003
- Trefethen and Bau, Numerical Linear Algebra