Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems

The Projected Aggregation methods generate the new point xk+1 as the projection of xk onto an "aggregate" hyperplane usually arising from linear combinations of the hyperplanes defined by the blocks. The aim of this paper is to improve the speed of convergence of a particular kind of them...

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Detalles Bibliográficos
Publicado: 2002
Materias:
Parallel iterative methods
Projected aggregation methods
Row partition strategies
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v117_n1-4_p95_Scolnik
http://hdl.handle.net/20.500.12110/paper_02545330_v117_n1-4_p95_Scolnik
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02545330_v117_n1-4_p95_Scolnik
record_format dspace
spelling paper:paper_02545330_v117_n1-4_p95_Scolnik2023-06-08T15:21:58Z Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems Parallel iterative methods Projected aggregation methods Row partition strategies The Projected Aggregation methods generate the new point xk+1 as the projection of xk onto an "aggregate" hyperplane usually arising from linear combinations of the hyperplanes defined by the blocks. The aim of this paper is to improve the speed of convergence of a particular kind of them by projecting the directions given by the blocks onto the aggregate hyperplane defined in the last iteration. For that purpose we apply the scheme introduced in "A new method for solving large sparse systems of linear equations using row projections" [11], for a given block projection algorithm, to some new methods here introduced whose main features are related to the fact that the projections do not need to be accurately computed. Adaptative splitting schemes are applied which take into account the structure and conditioning of the matrix. It is proved that these new highly parallel algorithms improve the original convergence rate and present numerical results which show their computational efficiency. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v117_n1-4_p95_Scolnik http://hdl.handle.net/20.500.12110/paper_02545330_v117_n1-4_p95_Scolnik
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Parallel iterative methods
Projected aggregation methods
Row partition strategies
spellingShingle Parallel iterative methods
Projected aggregation methods
Row partition strategies
Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
topic_facet Parallel iterative methods
Projected aggregation methods
Row partition strategies
description The Projected Aggregation methods generate the new point xk+1 as the projection of xk onto an "aggregate" hyperplane usually arising from linear combinations of the hyperplanes defined by the blocks. The aim of this paper is to improve the speed of convergence of a particular kind of them by projecting the directions given by the blocks onto the aggregate hyperplane defined in the last iteration. For that purpose we apply the scheme introduced in "A new method for solving large sparse systems of linear equations using row projections" [11], for a given block projection algorithm, to some new methods here introduced whose main features are related to the fact that the projections do not need to be accurately computed. Adaptative splitting schemes are applied which take into account the structure and conditioning of the matrix. It is proved that these new highly parallel algorithms improve the original convergence rate and present numerical results which show their computational efficiency.
title Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
title_short Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
title_full Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
title_fullStr Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
title_full_unstemmed Acceleration Scheme for Parallel Projected Aggregation Methods for Solving Large Linear Systems
title_sort acceleration scheme for parallel projected aggregation methods for solving large linear systems
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v117_n1-4_p95_Scolnik
http://hdl.handle.net/20.500.12110/paper_02545330_v117_n1-4_p95_Scolnik
_version_ 1768544638484873216

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