Thursday, October 30

Sparse Approximate Inverse Preconditioners (Part I of II)

3:00 PM-5:00 PM
Room: Ballroom 1

Recently, renewed interest in sparse approximate inverse preconditioners (SAIP) has emerged. The motivation for the renewed interest is largely from parallel processing. Many new techniques and results have been proposed in recent years for identifying an effective sparsity pattern of the approximation. The new insight to this "old" idea has offered new promise. Some difficult problems can be effectively solved using these new techniques. In this minisymposium, some of the leading experts in this field discuss new results and challenging problems. To construct a good, but sparse approximation depends on the sparsity pattern and initial approaches failed to provide a robust technique to determine an effective sparsity pattern. To reduce the cost of preconditioning, the sparse approximation has to be as sparse as possible. Unfortunately, this goal has to be balanced with the quality of the preconditioner since the inverse in general is a dense matrix. The search for an optimal sparsity pattern would be a much more expensive proposition than the solution itself. Effective heuristics are required and many open problems still remain to be resolved.

Organizer: Wei-Pai Tang
University of Waterloo, Canada

3:00 New Techniques and Applications for Approximate Inverse Preconditioning
Edmond Chow and Yousef Saad, University of Minnesota, Minneapolis
3:30 Ordering Techniques for Sparse Approximate Inverse Preconditioning
Robert E. Bridson, University of Waterloo, Canada; and Wei-Pai Tang, Organizer
4:00 A Comparative Study of Sparse Approximate Inverse Preconditioners
Michele Benzi, Los Alamos National Laboratory; and Miroslav Tuma, Czech Academy of Sciences, Czech Republic

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