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Explicit inverse of nonsingular Jacobi matrices
dc.contributor.author | Encinas Bachiller, Andrés Marcos |
dc.contributor.author | Jiménez Jiménez, María José |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2019-03-26T13:07:36Z |
dc.date.available | 2021-03-22T01:28:45Z |
dc.date.issued | 2019-06-30 |
dc.identifier.citation | Encinas, A.; Jiménez, M.J. Explicit inverse of nonsingular Jacobi matrices. "Discrete applied mathematics", 30 Juny 2019, vol. 263, p. 130-139. |
dc.identifier.issn | 0166-218X |
dc.identifier.other | http://arxiv.org/abs/1807.07642 |
dc.identifier.uri | http://hdl.handle.net/2117/130869 |
dc.description.abstract | We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of Sturm–Liouville boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout a discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provide the entries of the inverse matrix |
dc.format.extent | 10 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències |
dc.subject.lcsh | Differential equations, Linear |
dc.subject.lcsh | Jacobi method |
dc.subject.lcsh | Matrices |
dc.subject.other | Tridiagonal matrices |
dc.subject.other | Second order linear difference equations |
dc.subject.other | Sturm–Liouville boundary value problems |
dc.subject.other | Discrete Schrödinger operator |
dc.subject.other | Chebyshev functions and polynomials |
dc.title | Explicit inverse of nonsingular Jacobi matrices |
dc.type | Article |
dc.subject.lemac | Equacions diferencials lineals |
dc.subject.lemac | Matrius (Matemàtica) |
dc.contributor.group | Universitat Politècnica de Catalunya. MAPTHE - Anàlisi matricial i Teoria Discreta del Potencial |
dc.identifier.doi | 10.1016/j.dam.2019.03.005 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::15 Linear and multilinear algebra; matrix theory |
dc.subject.ams | Classificació AMS::39 Difference and functional equations::39A Difference equations |
dc.subject.ams | Classificació AMS::31 Potential theory |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/pii/S0166218X19301556 |
dc.rights.access | Open Access |
local.identifier.drac | 24011714 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2014-60450-R/ES/LA RESISTENCIA EFECTIVA COMO HERRAMIENTA PARA EL ESTUDIO DEL PROBLEMA INVERSO DE LAS CONDUCTANCIAS Y EL ANALISIS DE LAS PERTURBACIONES DE REDES/ |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-85996-R/ES/ANALISIS MULTIFACETICO DE PROBLEMAS INVERSOS EN REDES: AUTOVALORES, RECUPERACION DE LA CONDUCTANCIA E IMPLEMENTACION DE ALGORITMOS/ |
local.citation.author | Encinas, A.; Jiménez, M.J. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 263 |
local.citation.startingPage | 130 |
local.citation.endingPage | 139 |
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