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

As a generalization of k -tridiagonal matrices, many variations of ( p , q )-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n -square ( p , q )-tridiagonal matrices under a certain conditio...

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Vydáno v:Numerical algorithms Ročník 93; číslo 2; s. 899 - 917
Hlavní autoři: Jia, Ji-Teng, Xie, Rong, Xu, Xiao-Yan, Ni, Shuo, Wang, Jie
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2023
Springer Nature B.V
Témata:
Algebra
Algorithms
Banded structure
Boundary value problems
Computation
Computer Science
Matlab
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Theory of Computation
Tridiagonal matrices
Inverses
15A20
65F50
Bidiagonal matrices
Bidiagonalization
(
15B05
,
ISSN:1017-1398, 1572-9265
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Shrnutí:As a generalization of k -tridiagonal matrices, many variations of ( p , q )-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n -square ( p , q )-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function.
Bibliografie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01446-0