solving large eigenvalue problems. We will focus on the algorithms and the

applications of eigenvalue solvers. The assignments of this course require

programming ability on parallel environments, such as cluster or GPU.

Textbook:

Matrix Algorithms: Volume II: Eigensystems

Authors: G. W. Stewart

Topics:

1. Basic linear algebra review: LU, Cholesky, QR, Eigen-problems

2. Applications of eigenvalue and SVD

2.1 Pagerank and stationary probability

2.2 Physics problems

2.3 For graph partition

2.4 For dimension reduction

2.5 Others

3. Algorithms to solve eigenvalue problems

3.1 Power methods

3.2 QR methods

3.3 Methods for symmetric matrices and for SVD

3.4 Krylov/Lanczos methods

3.5 Restart algorithms

3.6 Deflation

3.7 Contour methods

3.8 Inexact methods

3.9 Others

Grading:

1. 3 Programming assignments: 45%

(a) ARPACK http://www.caam.rice.edu/software/ARPACK/

(b) Parallel ARPACK

(c) Solver on GPU

2. Class note: 30%

3. Final project: 25%