Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral
We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/5/870 |
| _version_ | 1797534300352020480 |
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| author | Diego Caratelli Paolo Emilio Ricci |
| author_facet | Diego Caratelli Paolo Emilio Ricci |
| author_sort | Diego Caratelli |
| collection | DOAJ |
| description | We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©. |
| first_indexed | 2024-03-10T11:27:39Z |
| format | Article |
| id | doaj.art-46fd215c36204c5fb73076b862a6e27c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:27:39Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-46fd215c36204c5fb73076b862a6e27c2023-11-21T19:30:19ZengMDPI AGSymmetry2073-89942021-05-0113587010.3390/sym13050870Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s IntegralDiego Caratelli0Paolo Emilio Ricci1Department of Research and Development, The Antenna Company, High Tech Campus 29, 5656 AE Eindhoven, The NetherlandsSection of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyWe show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.https://www.mdpi.com/2073-8994/13/5/870Dunford-Taylor’s integralmatrix functionstridiagonal matrixmatrix inversion |
| spellingShingle | Diego Caratelli Paolo Emilio Ricci Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral Symmetry Dunford-Taylor’s integral matrix functions tridiagonal matrix matrix inversion |
| title | Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral |
| title_full | Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral |
| title_fullStr | Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral |
| title_full_unstemmed | Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral |
| title_short | Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral |
| title_sort | inversion of tridiagonal matrices using the dunford taylor s integral |
| topic | Dunford-Taylor’s integral matrix functions tridiagonal matrix matrix inversion |
| url | https://www.mdpi.com/2073-8994/13/5/870 |
| work_keys_str_mv | AT diegocaratelli inversionoftridiagonalmatricesusingthedunfordtaylorsintegral AT paoloemilioricci inversionoftridiagonalmatricesusingthedunfordtaylorsintegral |