Parallel projected aggregation methods for solving large inconsistent systems

The Projected Aggregation Methods (PAM) for solving linear systems of equali- ties and/or inequalities, generate a new iterate xk+1 by projecting the current point xk onto a separating hyperplane generated by a given linear combination of the original hyperplanes and/or halfspaces. In [9, 16, 17, 18...

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Detalles Bibliográficos
Autor principal: Scolnik, Hugo Daniel
Formato: Objeto de conferencia
Lenguaje:Inglés
Publicado: 2003
Materias:
Ciencias Informáticas
Parallel
Projected Aggregation Methods
Incomplete Projections
Inconsistent System
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/22894
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-22894
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Informáticas
Parallel
Projected Aggregation Methods
Incomplete Projections
Inconsistent System
spellingShingle Ciencias Informáticas
Parallel
Projected Aggregation Methods
Incomplete Projections
Inconsistent System
Scolnik, Hugo Daniel
Parallel projected aggregation methods for solving large inconsistent systems
topic_facet Ciencias Informáticas
Parallel
Projected Aggregation Methods
Incomplete Projections
Inconsistent System
description The Projected Aggregation Methods (PAM) for solving linear systems of equali- ties and/or inequalities, generate a new iterate xk+1 by projecting the current point xk onto a separating hyperplane generated by a given linear combination of the original hyperplanes and/or halfspaces. In [9, 16, 17, 18] we introduced acceleration schemes for solving linear systems within a PAM like framework. The basic idea was to force the next iterate to belong to the convex region de ned by the new separating/or aggregated hyperplane computed in the previous iteration. In this paper we extend the above mentioned methods to the problem of nding the least squares solution to inconsistent systems. In the new algorithm we used a scheme of incomplete alternate projections for minimizing the proximity function, similar to the one of Csisz ar y Tusn ady described in [4] which uses exact projections. The parallel simultaneous projection ACCIM algorithm in [16] is very eÆcient for ob- taining approximations with suitable properties, and is the basis for calculating the incomplete intermediate projections. We discuss the convergence properties of the new algorithm and also present numerical experiences obtained by applying it to image reconstruction problems using the SNARK93 system [3].
format Objeto de conferencia
Objeto de conferencia
author Scolnik, Hugo Daniel
author_facet Scolnik, Hugo Daniel
author_sort Scolnik, Hugo Daniel
title Parallel projected aggregation methods for solving large inconsistent systems
title_short Parallel projected aggregation methods for solving large inconsistent systems
title_full Parallel projected aggregation methods for solving large inconsistent systems
title_fullStr Parallel projected aggregation methods for solving large inconsistent systems
title_full_unstemmed Parallel projected aggregation methods for solving large inconsistent systems
title_sort parallel projected aggregation methods for solving large inconsistent systems
publishDate 2003
url http://sedici.unlp.edu.ar/handle/10915/22894
work_keys_str_mv AT scolnikhugodaniel parallelprojectedaggregationmethodsforsolvinglargeinconsistentsystems
bdutipo_str Repositorios
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