A tridiagonalization-based numerical algorithm for computing the inverses of (p, q)-pentadiagonal matrices

Matrix inverse computation is one of the fundamental mathematical problems of numerical linear algebra and has been widely used in various fields of computer science and engineering. In the current paper, a reliable and efficient algorithm is presented for numerically computing the inverses of n -sq...

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Vydané v:Computational & applied mathematics Ročník 42; číslo 4
Hlavní autori: Wang, Jie, Jia, Ji-Teng, Xie, Rong
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.06.2023
Predmet:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Tridiagonal matrices
Inverses
15A20
65F50
65F40
Block diagonalization
Tridiagonalization
15A15
Pentadiagonal matrices
ISSN:2238-3603, 1807-0302
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Popis
Shrnutí:Matrix inverse computation is one of the fundamental mathematical problems of numerical linear algebra and has been widely used in various fields of computer science and engineering. In the current paper, a reliable and efficient algorithm is presented for numerically computing the inverses of n -square ( p , q )-pentadiagonal matrices. The algorithm is based on the combination of a tridiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general tridiagonal matrices. The experimental results of some representative numerical examples are provided to demonstrate the performance and effectiveness of the proposed algorithm and its competitiveness with MATLAB built-in function.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02305-x