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Compact quasi-Newton preconditioners for symmetric positive definite linear systems

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Compact quasi-Newton preconditioners for symmetric positive definite linear systems

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dc.contributor.author BERGAMASCHI, LUCA es_ES
dc.contributor.author Marín Mateos-Aparicio, José es_ES
dc.contributor.author MARTINEZ, ANGELES es_ES
dc.date.accessioned 2021-02-25T04:49:42Z
dc.date.available 2021-02-25T04:49:42Z
dc.date.issued 2020-12 es_ES
dc.identifier.issn 1070-5325 es_ES
dc.identifier.uri http://hdl.handle.net/10251/162373
dc.description.abstract [EN] In this paper, preconditioners for the conjugate gradient method are studied to solve the Newton system with symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of Symmetric Rank one (SR1) and Broyden-Fletcher-Goldfarb-Shanno (BFGS) low-rank updates. We develop conditions under which the SR1 update maintains the preconditioner symmetric positive definite. Spectral analysis of the SR1 preconditioned Jacobians shows an improved eigenvalue distribution as the Newton iteration proceeds. A compact matrix formulation of the preconditioner update is developed which reduces the cost of its application and is more suitable to parallel implementation. Some notes on the implementation of the corresponding Inexact Newton method are given and some numerical results on a number of model problems illustrate the efficiency of the proposed preconditioners. es_ES
dc.description.sponsorship This work was supported by the Spanish Ministerio de Economia y Competitividad under grants MTM2014-58159-P, MTM2017-85669-P, and MTM2017-90682-REDT. The first and third authors have been also partially supported by the INdAM Research group GNCS, 2020 Project: Optimization and advanced linear algebra for problems arising from PDEs. es_ES
dc.language Inglés es_ES
dc.publisher John Wiley & Sons es_ES
dc.relation.ispartof Numerical Linear Algebra with Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Conjugate gradient es_ES
dc.subject Inexact Newton method es_ES
dc.subject Quasi-Newton matrices es_ES
dc.subject Sequence of preconditioners es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Compact quasi-Newton preconditioners for symmetric positive definite linear systems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1002/nla.2322 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI//MTM2017-90682-REDT/ES/RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-85669-P/ES/PROBLEMAS MATRICIALES: COMPUTACION, TEORIA Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-58159-P/ES/PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICAS/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bergamaschi, L.; Marín Mateos-Aparicio, J.; Martinez, A. (2020). Compact quasi-Newton preconditioners for symmetric positive definite linear systems. Numerical Linear Algebra with Applications. 27(6):1-17. https://doi.org/10.1002/nla.2322 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1002/nla.2322 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 17 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 27 es_ES
dc.description.issue 6 es_ES
dc.relation.pasarela S\422728 es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
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