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Vaidya's preconditioners: implementation and experimental study (2001).
| Content Provider | CiteSeerX |
|---|---|
| Author | Chen, Doron Toledo, Sivan |
| Abstract | We describe the implementation and performance of a novel class of preconditioners. These preconditioners were proposed and theoretically analyzed by Pravin Vaidya in 1991, but no report on their implementation or performance in practice has ever been published. We show experimentally that these preconditioners have some remarkable properties. We show that within the class of diagonally-dominant symmetric matrices, the cost and convergence of these preconditioners depends almost only on the nonzero structure of the matrix, but not on its numerical values. In particular, this property leads to robust convergence behavior on di#cult 3-dimensional problems that cause stagnation in incomplete-Cholesky preconditioners (more specifically, in drop-tolerance incomplete Cholesky without diagonal modification, with diagonal modification, and with relaxed diagonal modification). On such problems, we have observed cases in which a Vaidya-preconditioned solver is more than 6 times faster than an incomplete-Cholesky-preconditioned solver, when we allow similar amounts of fill in the factors of both preconditioners. We also show that Vaidya's preconditioners perform and scale similarly or better than drop-tolerance relaxed-modified incomplete Cholesky preconditioners on a wide range of 2-dimensional problems. In particular, on anisotropic 2D problems, Vaidya delivers robust convergence independently of the direction of anisotropy and the ordering of the unknowns. However, on many 3D problems in which incomplete-Choleskypreconditioned solvers converge without stagnating, Vaidya-preconditioned solvers are much slower. We also show how the insights gained from this study can be used to design faster and more robust solvers for some di#cult problems. 1. |
| File Format | |
| Publisher Date | 2001-01-01 |
| Access Restriction | Open |
| Subject Keyword | Experimental Study Vaidya-preconditioned Solver Diagonal Modification Incomplete-choleskypreconditioned Solver Drop-tolerance Relaxed-modified Incomplete Cholesky Preconditioners Di Cult 3-dimensional Problem Wide Range Robust Solver Robust Convergence Drop-tolerance Incomplete Cholesky Nonzero Structure Diagonally-dominant Symmetric Matrix Novel Class Remarkable Property Di Cult Problem Incomplete-cholesky-preconditioned Solver Relaxed Diagonal Modification Incomplete-cholesky Preconditioners Pravin Vaidya 2-dimensional Problem Similar Amount Numerical Value Convergence Behavior |
| Content Type | Text |
