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

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dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author González Pizarro, Javier Andrés
dc.date.accessioned 2021-03-22T10:44:49Z
dc.date.available 2021-03-22T10:44:49Z
dc.date.issued 2019-01
dc.identifier.bibliographicCitation Dopico, 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.
dc.identifier.issn 1070-5325
dc.identifier.uri http://hdl.handle.net/10016/32194
dc.description.abstract In 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.
dc.format.extent 26
dc.language.iso eng
dc.publisher Wiley
dc.rights © 2018 John Wiley & Sons, Ltd.
dc.subject.other Large-scale
dc.subject.other Linearization
dc.subject.other Rational eigenvalue problem
dc.subject.other Rational Krylov method
dc.subject.other Arnoldi method
dc.subject.other Linearizations
dc.title A compact rational Krylov method for large-scale rational eigenvalue problems
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1002/nla.2214
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.relation.projectID Gobierno de España. MTM2015-68805-REDT
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 26
dc.identifier.publicationtitle Numerical Linear Algebra with Applications
dc.identifier.publicationvolume 26
dc.identifier.uxxi AR/0000022602
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades (España)
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señales
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