CS 290H, Fall 2004: Final Project Ideas

These are just ideas -- please see me if there's something else you'd like to work on, or if you'd like to discuss any of these. Let me know by Friday 29 October what your project will be and who will be working on it.

Each project must turn in a half-page progress report by Tuesday 16 November, and a final report of 5-10 pages by Wednesday 8 December. Survey projects will also include a 20-minute presentation during the last week of class, 30 November or 2 December.

Survey projects must be solo. Experimental projects can be solo or a group of two students.

Survey projects. For a survey project, you will read two or three papers on a sparse matrix topic not covered in class. Here are some possibilites; I can send you the references to the papers for any of them. Email me if you're interested in something not on the list.

• Symmetric indefinite factorization: A = L*D*L' where D is block diagonal with 1-by-1 and 2-by-2 blocks.
• Sparse QR factorization and least squares problems.
• The real details of UMFpack, Tim Davis's unsymmetric multifrontal method.
• Mesh partitioning algorithms: geometric, spectral, multilevel.
• Implementations of minimum degree: AMD, Liu's minimum degree, minimum deficiency.
• Elimination orders that attempt to minimize bandwidth front size.
• Parallel multifrontal algorithms, e.g. MUMPS.
• Graph coloring for sparse Jacobian estimation.

Algorithm experiments. For an algorithm experiment, you will implement and compare different approaches to a sparse algorithm. Here are some possibilities; email me if you're interested in something not on the list.

• What's the best way to do memory allocation for sparse matrix * sparse matrix? Look at two-pass strategies, probabilistic prediction (Cohen paper), etc.
• Devise and experiment with hill-climbing strategies that take a specified elimination order and try to improve it.
• Implement the nearly-linear-time row and column count algorithms, and compare their performance with Matlab's (which uses a less sophisticated approach).
• Experiment with data structures for right-looking LU factorization, trying to match performance of Matlab's GPmod and KLU.
• Write a drop-tolerance incomplete factorization preconditioner for Matlab, and experiment with using it in an iterative method.
• Write a graphic sparse matrix explorer for Matlab that is more flexible and useful than "spy".

Application experiments. An application experiment is any problem that comes from computational science and has a sparse matrix computation in it; you will experiment with ways to do the sparse computation. The application should be one you are already familiar with, from your research or another class or a collaboration. Talk to me if you'd like to do this.