The path resistance method for bounding &lgr;2 of a Laplacian
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Combinatorics, Probability and Computing
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Combinatorics, Probability and Computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Algebraic analysis of high-pass quantization
ACM Transactions on Graphics (TOG)
Study of Parallel Linear Solvers for Three-Dimensional Subsurface Flow Problems
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Parallel support graph preconditioners
HiPC'06 Proceedings of the 13th international conference on High Performance Computing
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
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.