This goal of this semester is to study the numerical algorithms for 
<br>solving large eigenvalue problems.  We will focus on the algorithms and the 
<br>applications of eigenvalue solvers. The assignments of this course require 
<br>programming ability on parallel environments, such as cluster or GPU.
<br>
<br>Textbook: 
<br>Matrix Algorithms: Volume II: Eigensystems
<br>Authors: G. W. Stewart
<br>
<br>Topics:
<br>1. Basic linear algebra review: LU, Cholesky, QR, Eigen-problems
<br>2. Applications of eigenvalue and SVD
<br>2.1 Pagerank and stationary probability
<br>2.2 Physics problems
<br>2.3 For graph partition
<br>2.4 For dimension reduction 
<br>2.5 Others
<br>3. Algorithms to solve eigenvalue problems
<br>3.1 Power methods
<br>3.2 QR methods
<br>3.3 Methods for symmetric matrices and for SVD
<br>3.4 Krylov/Lanczos methods
<br>3.5 Restart algorithms
<br>3.6 Deflation
<br>3.7 Contour methods
<br>3.8 Inexact methods
<br>3.9 Others
<br>
<br>Grading:
<br>1. 3 Programming assignments: 45%
<br>   (a) ARPACK http://www.caam.rice.edu/software/ARPACK/
<br>   (b) Parallel ARPACK
<br>   (c) Solver on GPU 
<br>2. Class note: 30%
<br>3. Final project: 25% 
<br>