Performance Evaluation of a New Parallel Preconditioner School of Computer Science

The linear systems associated with large, sparse, symmetric, positive definite matrices are often solved iteratively using the pre-conditioned conjugate gradient method. We have developed a new class of preconditioners, support tree preconditioners, that are based on the connectivity of the graphs corresponding to the matrices and are well-structured for parallel implementation. In this paper, we evaluate the performance of support tree precondi-tioners by comparing them against two common types of precon-ditioners: diagonal scaling, and incomplete Cholesky. Support tree preconditioners require less overall storage and less work per iteration than incomplete Cholesky preconditioners. In terms of total execution time, support tree preconditioners outperform both diagonal scaling and incomplete Cholesky preconditioners.