Explicit inverse of nonsingular Jacobi matrices
| Autor: | M. J. Jiménez, A. M. Encinas |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. MAPTHE - Anàlisi matricial i Teoria Discreta del Potencial |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
15B99
31E05 39A06 0211 other engineering and technologies Inverse 0102 computer and information sciences 02 engineering and technology Matrius (Matemàtica) 01 natural sciences law.invention symbols.namesake Matrix (mathematics) Matrices law Tridiagonal matrices matrix theory FOS: Mathematics Discrete Mathematics and Combinatorics Applied mathematics Mathematics - Combinatorics Boundary value problem Uniqueness Mathematics - Numerical Analysis Jacobi method Second order linear difference equations Sturm–Liouville boundary value problems Mathematics Tridiagonal matrix Applied Mathematics Operator (physics) 15 Linear and multilinear algebra matrix theory [Classificació AMS] 15 Linear and multilinear algebra [Classificació AMS] Discrete Schrödinger operator 021107 urban & regional planning 39 Difference and functional equations::39A Difference equations [Classificació AMS] Mathematics - Rings and Algebras Numerical Analysis (math.NA) 31 Potential theory [Classificació AMS] Invertible matrix 010201 computation theory & mathematics Rings and Algebras (math.RA) Chebyshev functions and polynomials Equacions diferencials lineals symbols Differential equations Linear Combinatorics (math.CO) Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències [Àrees temàtiques de la UPC] Schrödinger's cat |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| DOI: | 10.1016/j.dam.2019.03.005 |
| Popis: | 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 Schr\"odinger 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 provides the entries of the inverse matrix. Comment: The article will appear in Discrete Applied Mathematics |
| Databáze: | OpenAIRE |
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