Laurent expansion of the inverse of perturbed, singular matrices

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dc.contributor.author González Rodríguez, Pedro
dc.contributor.author Moscoso Castro, Miguel Ángel
dc.contributor.author Kindelan Segura, Manuel
dc.date.accessioned 2016-09-14T10:14:59Z
dc.date.available 2017-10-15T22:00:04Z
dc.date.issued 2015-10-15
dc.identifier.bibliographicCitation Journal of Computational Physics, 2015, 299, pp. 307–319.
dc.identifier.issn 0021-9991
dc.identifier.uri http://hdl.handle.net/10016/23560
dc.description.abstract In this paper we describe a numerical algorithm to compute the Laurent expansion of the inverse of singularly perturbed matrices. The algorithm is based on the resolvent formalism used in complex analysis to study the spectrum of matrices. The input of the algorithm are the matrix coefficients of the power series expansion of the perturbed matrix. The matrix coefficients of the Laurent expansion of the inverse are computed using recursive analytical formulae. We show that the computational complexity of the proposed algorithm grows algebraically with the size of the matrix, but exponentially with the order of the singularity. We apply this algorithm to several matrices that arise in applications. We make special emphasis to interpolation problems with radial basis functions.
dc.description.sponsorship This work has been supported by Spanish MICINN Grants FIS2013-41802-R and CSD2010-00011.
dc.format.extent 13
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier 2015
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Laurent series
dc.subject.other Inverse
dc.subject.other Radial basis functions
dc.subject.other Interpolation
dc.title Laurent expansion of the inverse of perturbed, singular matrices
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jcp.2015.07.006
dc.subject.eciencia Biología y Biomedicina
dc.identifier.doi 10.1016/j.jcp.2015.07.006
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. FIS-2013-41802-R
dc.relation.projectID Gobierno de España. CSD2010-00011
dc.type.version acceptedVersion
dc.relation.eventtype proceeding
dc.identifier.publicationfirstpage 307
dc.identifier.publicationlastpage 319
dc.identifier.publicationtitle Journal of computational physics
dc.identifier.publicationvolume 299
dc.identifier.uxxi AR/0000016824
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