Linear Algebraic Computation on Distributed Memory Parallel Machines

摘要

The project entailed investigating several problems in the parallel solution ofsparse systems of linear equations and eigenproblems, including: algorithms for factoring sparse matrices; techniques for the solution of sparse triangular systems; iterative methods for sparse systems, focusing mainly on preconditioning techniques for conjugate-direction methods; the solution of the symmetric tridiagonal eigenproblem. While this may seem to be an eclectic group of topics, there are, in fact, close relationships among them. As one example, a common technique for preconditioning iterative methods depends crucially on efficient solution of triangular systems. As another, it should be possible to construct an effective Lanczos-type algorithm for sparse, symmetric eigenproblems by combining the techniques required for conjugate-direction iterations for linear systems with those required for the solution of symmetric tridiagonal eigenproblems. (AN).