Performance evaluation of a new parallel preconditioner

The linear systems associated with large, sparse, symmetric, positive definite matrices are often solved iteratively using the preconditioned 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. We evaluate the performance of support tree preconditioners by comparing them against two common types of preconditioners: 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