dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. MAPTHE - Anàlisi matricial i Teoria Discreta del Potencial
dc.contributor.author
Encinas Bachiller, Andrés Marcos
dc.contributor.author
Jiménez Jiménez, María José
dc.date.issued
2019-06-30
dc.identifier
Encinas, A.; Jiménez, M.J. Explicit inverse of nonsingular Jacobi matrices. "Discrete applied mathematics", 30 Juny 2019, vol. 263, p. 130-139.
dc.identifier
http://arxiv.org/abs/1807.07642
dc.identifier
https://hdl.handle.net/2117/130869
dc.identifier
10.1016/j.dam.2019.03.005
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.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://www.sciencedirect.com/science/article/pii/S0166218X19301556
dc.relation
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
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/
dc.rights
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights
Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
dc.subject
Differential equations, Linear
dc.subject
Tridiagonal matrices
dc.subject
Second order linear difference equations
dc.subject
Sturm–Liouville boundary value problems
dc.subject
Discrete Schrödinger operator
dc.subject
Chebyshev functions and polynomials
dc.subject
Equacions diferencials lineals
dc.subject
Matrius (Matemàtica)
dc.subject
Classificació AMS::15 Linear and multilinear algebra; matrix theory
dc.subject
Classificació AMS::39 Difference and functional equations::39A Difference equations
dc.subject
Classificació AMS::31 Potential theory
dc.title
Explicit inverse of nonsingular Jacobi matrices
