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A compact rational Krylov method for large-scale rational eigenvalue problems

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señaleses
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.authorGonzález Pizarro, Javier Andrés
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (España)es
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-03-22T10:44:49Z
dc.date.available2021-03-22T10:44:49Z
dc.date.issued2019-01
dc.description.abstractIn this work, we propose a new method, termed as R-CORK, for the numerical solution of large-scale rational eigenvalue problems, which is based on a linearization and on a compact decomposition of the rational Krylov subspaces corresponding to this linearization. R-CORK is an extension of the compact rational Krylov method (CORK) introduced very recently in the literature to solve a family of nonlinear eigenvalue problems that can be expressed and linearized in certain particular ways and which include arbitrary polynomial eigenvalue problems, but not arbitrary rational eigenvalue problems. The R-CORK method exploits the structure of the linearized problem by representing the Krylov vectors in a compact form in order to reduce the cost of storage, resulting in a method with two levels of orthogonalization. The first level of orthogonalization works with vectors of the same size as the original problem, and the second level works with vectors of size much smaller than the original problem. Since vectors of the size of the linearization are never stored or orthogonalized, R-CORK is more efficient from the point of view of memory and orthogonalization than the classical rational Krylov method applied directly to the linearization. Taking into account that the R-CORK method is based on a classical rational Krylov method, to implement implicit restarting is also possible, and we show how to do it in a memory-efficient way. Finally, some numerical examples are included in order to show that the R-CORK method performs satisfactorily in practice.en
dc.format.extent26
dc.identifier.bibliographicCitationDopico, F. M. & González‐Pizarro, J. (2018). A compact rational Krylov method for large‐scale rational eigenvalue problems. Numerical Linear Algebra with Applications, 26(1), e2214.en
dc.identifier.doihttps://doi.org/10.1002/nla.2214
dc.identifier.issn1070-5325
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue1
dc.identifier.publicationlastpage26
dc.identifier.publicationtitleNumerical Linear Algebra with Applicationsen
dc.identifier.publicationvolume26
dc.identifier.urihttps://hdl.handle.net/10016/32194
dc.identifier.uxxiAR/0000022602
dc.language.isoeng
dc.publisherWileyen
dc.relation.projectIDGobierno de España. MTM2012-32542es
dc.relation.projectIDGobierno de España. MTM2015-65798-Pes
dc.relation.projectIDGobierno de España. MTM2017-90682-REDTes
dc.relation.projectIDGobierno de España. MTM2015-68805-REDTes
dc.rights© 2018 John Wiley & Sons, Ltd.es
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherLarge-scaleen
dc.subject.otherLinearizationen
dc.subject.otherRational eigenvalue problemen
dc.subject.otherRational Krylov methoden
dc.subject.otherArnoldi methoden
dc.subject.otherLinearizationsen
dc.titleA compact rational Krylov method for large-scale rational eigenvalue problemsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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