An incomplete projections algorithm for solving large inconsistent linear systems

dc.creatorScolnik, Hugo Daniel
dc.creatorEchebest, Nélida Ester
dc.creatorGuardarucci, María Teresa
dc.creatorVacchino, María Cristina
dc.date2005
dc.date2023-03-14T14:26:54Z
dc.date.accessioned2023-07-15T09:49:57Z
dc.date.available2023-07-15T09:49:57Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/150084
dc.identifierissn:0716-7563
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7489568
dc.descriptionThe 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.
dc.descriptionFacultad de Ciencias Exactas
dc.formatapplication/pdf
dc.format61-71
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.subjectMatemática
dc.subjectProjected aggregation methods
dc.subjectIncomplete projections
dc.subjectInconsistent system
dc.titleAn incomplete projections algorithm for solving large inconsistent linear systems
dc.typeArticulo
dc.typeArticulo


Este ítem pertenece a la siguiente institución