ECS 231 Homework 3 Assignment
Due Feburary 19, 2013

Iterative Subspace Projection Methods for solving large scale linear systems

• Purpose: Iterative subspace projection methods are most widely used methods for solving large sparse linear systems A x = b. In this project, you will implement
  1. SD and CG methods
  2. MD and GMRES methods
  and observe the convergence behaviors of these methods.
  

• Details
  • Implement the methods
    
    • If you use Matlab, you may not use Matlab's functions ``cg'' and ``gmress'', You should write your own functions ``mycg.m'' and ``mygmres.m''.
    • If you use C or FORTRAN, you can start with the Templates.
      
  • Run your implementations on the following test matrices, available from Matrix Market.
    • SPD matrices:bcsstk15 and NOS3 for SD and CG
    • Nonsymmetric matrices: WEST0479 and MAHINDAS for MR and GMRES
  • Report your implementations and numerical findings by including the following components:
    1. Abstract/executive summary
    2. Provide a high-level description of algorthm in pseudo-code style (it's fine if you copy heavily from lecture notes or other sources, just make sure to be self-content and provide citation)
    3. Discuss implementation details, such as how to access the matrix, stopping criterion, and accuracy assessment
    4. Present numerical experiment results, illustrate the convergence behaviors of SD and CG in plot, and MD and GMRES in another plot.
    5. Acknowledgment and references
    6. Appendix: the code
  • Please limit to your report within 6 pages.

• Resources
  • Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
  • Matrix Market from NIST
  • The University of Florida Sparse Matrix Collection
  • Iterative methods in DOE ACTS collection