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...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-05, Vol.13 (5), p.870
Main Authors: Caratelli, Diego, Ricci, Paolo Emilio
Format: Article
Language:English
Subjects:
Applied mathematics
Computer algebra
Dunford-Taylor’s integral
Eigenvalues
Functional analysis
Integrals
Mathematical analysis
matrix functions
matrix inversion
Matrix methods
Ordinary differential equations
Partial differential equations
tridiagonal matrix
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Summary: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©.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13050870