An efficient breakdown-free algorithm for numerically evaluating the determinants of (p, q)-pentadiagonal matrices

( p , q )-Pentadiagonal matrices have received considerable attention in recent years, which are a generalization of pentadiagonal matrices. In this paper, a breakdown-free algorithm is presented for numerically evaluating the determinants of n -by- n ( p , q )-pentadiagonal matrices. The algorithm...

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Published inNumerical algorithms Vol. 97; no. 4; pp. 2031 - 2049
Main Authors Jia, Ji-Teng, Xie, Rong, Ni, Shuo, Xu, Xiao-Yan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Subjects
Algebra
Algorithms
Banded structure
Breakdown
Computer Science
Determinants
Eigenvalues
Linear algebra
Numeric Computing
Numerical Analysis
Original Paper
Software
Theory of Computation
 
Tridiagonal matrices
15A20
65F50
65F40
Block diagonalization
Tridiagonalization
(
Determinants
15A15
Pentadiagonal matrices
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ISSN1017-1398
1572-9265
DOI10.1007/s11075-024-01777-0

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Summary:( p , q )-Pentadiagonal matrices have received considerable attention in recent years, which are a generalization of pentadiagonal matrices. In this paper, a breakdown-free algorithm is presented for numerically evaluating the determinants of n -by- n ( p , q )-pentadiagonal matrices. The algorithm is based on the use of a reliable tridiagonalization process which preserves the banded structure and sparsity of the original matrix. Numerical examples are given in order to illustrate the effectiveness of the proposed algorithm. All of the experiments are performed on a computer with the aid of programs written in MATLAB.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01777-0