Parallel and Systolic Solution of Normalized Explicit Approximate Inverse Preconditioning
| Autor: | George A. Gravvanis, O. B. Efremides, Michael P. Bekakos, Konstantinos M. Giannoutakis |
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| Rok vydání: | 2004 |
| Předmět: |
Mathematical optimization
Partial differential equation Computer science Linear system MathematicsofComputing_NUMERICALANALYSIS Inverse Theoretical Computer Science Matrix (mathematics) Rate of convergence Factorization Hardware and Architecture Conjugate gradient method Applied mathematics Boundary value problem Finite difference discretization Software Information Systems |
| Zdroj: | The Journal of Supercomputing. 30:77-96 |
| ISSN: | 0920-8542 |
| DOI: | 10.1023/b:supe.0000040610.88224.7e |
| Popis: | A new class of normalized approximate inverse matrix techniques, based on the concept of sparse normalized approximate factorization procedures are introduced for solving sparse linear systems derived from the finite difference discretization of partial differential equations. Normalized explicit preconditioned conjugate gradient type methods in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of sparse linear systems. Theoretical results on the rate of convergence of the normalized explicit preconditioned conjugate gradient scheme and estimates of the required computational work are presented. Application of the new proposed methods on two dimensional initial/boundary value problems is discussed and numerical results are given. The parallel and systolic implementation of the dominant computational part is also investigated. |
| Databáze: | OpenAIRE |
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