Parallel Sparse Matrix Computations

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This project investigates the design, implementation, analysis of algorithms for several problems that arise in the solution of large, sparse systems of equations and least squares problems on high-performance parallel computers. The irregular nature of the memory access required by sparse matrix algorithms makes good performance difficult to achieve. Innovative algorithmic approaches capable of better concurrency than the traditional sequential approaches, and implementations that exploit the memory hierarchy are essential to obtain good performance. The following problems are being investigated: (1) An algebraic approach to the partitioning problem that arises in partitioning data and computation on parallel computers, and in computing nested dissection orderings, (2) The problem of reordering sparse matrices to minimize with applications to computing incomplete factorization (3) The product-form-inverse approach to the solution of sparse triangular systems on parallel computers, (4) The solution of rank-deficient least-squares problems on sequential and parallel computers.