CS-5911

Iterative Methods

Fall 2002

Quick Info

This class will introduce iterative methods in numerical linear algebra including standard methods (Jacobi, Gauss-Seidel, SOR), projection methods (steepest descent), and Krylov space methods (Arnoldi, Lanczos, CG, GMRES, QMR). Other topics include preconditioning and parallel implementations, and eigenvalue problems. If time permits we will also study iterative techniques for solving nonlinear problems.

We shall use the following texts:

``Iterative Methods for Solving Linear Systems '' by Anne Greenbaum, SIAM, Philadelphia, 1997.
``Iterative Methods for Sparse Linear Systems'' by Youssef Saad, WPS, 1996. This book is made publicly available by the author:
- Download Part 1 ( ps.gz or pdf)
- Download Part 2 ( ps.gz or pdf)
- Download Part 3 ( ps.gz or pdf)
- Download Part 4 ( ps.gz or pdf)
``Numerical methods for eigenvalue problems'' by Youssef Saad, Manchester University Press, 1992. This book is made publicly available by the author:
- Download Part 1 ( ps.gz or pdf)
- Download Part 2 ( ps.gz or pdf)
- Download Part 3 ( ps.gz or pdf)
- Download Part 4 ( ps.gz or pdf)
Matlab primer ( ps)
Additional materials will be given in class. Some of them may be found below.

If you have questions, come and see me in 226C Fisher every Tuesday after class. If you cannot make it, please send me e-mail to arrange for a mutual aggreeable time.

For detailed information please consult the syllabus ( PDF).

There will be several homework projects, on which the final grade will be based.

Homework

Please check the list of assignments.

Downloads

Chapter 4: Basic Iterations ( matlab code)
Oct 10. Implement LU decomposition ( example); Orthogonalization by modified Gram-Schmidt, QR decomposition( example); Residual norm steepest descent; Full orthogonalization method.
A set of large, sparse matrices from MatrixMarket ( information and the tarred, gzipped code).
Harwell MA28 sparse solver ( harwell.tar.gz).