An incomplete projections algorithm for solving large inconsistent linear systems

The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes and/or halfspaces. The authors have...

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Autores principales: Scolnik, Hugo Daniel, Echebest, Nélida Ester, Guardarucci, María Teresa, Vacchino, María Cristina
Formato: Articulo
Lenguaje:Inglés
Publicado: 2005
Materias:
Matemática
Projected aggregation methods
Incomplete projections
Inconsistent system
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/150084
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-150084
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Projected aggregation methods
Incomplete projections
Inconsistent system
spellingShingle Matemática
Projected aggregation methods
Incomplete projections
Inconsistent system
Scolnik, Hugo Daniel
Echebest, Nélida Ester
Guardarucci, María Teresa
Vacchino, María Cristina
An incomplete projections algorithm for solving large inconsistent linear systems
topic_facet Matemática
Projected aggregation methods
Incomplete projections
Inconsistent system
description The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x k+1 by projecting the current point x k onto a separating hyperplane generated by a given linear combination of the original hyperplanes and/or halfspaces. The authors have introduced in several papers new acceleration schemes for solving systems of linear equations and inequalities respectively, within a PAM like framework. The basic idea was to force the next iterate to belong to the convex region defined by the new separating or aggregated hyperplane computed in the previous iteration. In this paper the above mentioned methods are extended to the problem of finding the least squares solution to inconsistent systems. The new algorithm is based upon a new scheme of incomplete alternate projections for minimizing the proximity function. The parallel simultaneous projections ACCIM algorithm, published by the authors, is the basis for calculating the incomplete intermediate projections. The convergence properties of the new algorithm are given together with numerical experiences obtained by applying it to image reconstruction problems using the SNARKQ3 system.
format Articulo
Articulo
author Scolnik, Hugo Daniel
Echebest, Nélida Ester
Guardarucci, María Teresa
Vacchino, María Cristina
author_facet Scolnik, Hugo Daniel
Echebest, Nélida Ester
Guardarucci, María Teresa
Vacchino, María Cristina
author_sort Scolnik, Hugo Daniel
title An incomplete projections algorithm for solving large inconsistent linear systems
title_short An incomplete projections algorithm for solving large inconsistent linear systems
title_full An incomplete projections algorithm for solving large inconsistent linear systems
title_fullStr An incomplete projections algorithm for solving large inconsistent linear systems
title_full_unstemmed An incomplete projections algorithm for solving large inconsistent linear systems
title_sort incomplete projections algorithm for solving large inconsistent linear systems
publishDate 2005
url http://sedici.unlp.edu.ar/handle/10915/150084
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