Explicit inverse of nonsingular Jacobi matrices
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 linea...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/130869 |
| Acceso en línea: | https://hdl.handle.net/2117/130869 https://dx.doi.org/10.1016/j.dam.2019.03.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Linear Jacobi method Matrices Tridiagonal matrices Second order linear difference equations Sturm–Liouville boundary value problems Discrete Schrödinger operator Chebyshev functions and polynomials Equacions diferencials lineals Matrius (Matemàtica) Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::39 Difference and functional equations::39A Difference equations Classificació AMS::31 Potential theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències |
| Sumario: | 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 |
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