A cost-efficient numerical algorithm for the determinants of heptadiagonal matrices with Toeplitz structure

As a specific kind of banded matrices, heptadiagonal matrices arise frequently in a variety of fields in theoretical and computational chemistry. In this paper, we present a fast and reliable algorithm for numerically evaluating the determinants of heptadiagonal Toeplitz matrices by a certain type o...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2023-07, Vol.61 (6), p.1275-1291
Main Authors: Jia, Ji-Teng, Wang, Fu-Rong
Format: Article
Language:English
Subjects:
Algorithms
Chemistry
Chemistry and Materials Science
Computational chemistry
Determinants
Gaussian elimination
Iterative methods
Linear transformations
Math. Applications in Chemistry
Mathematical analysis
Numerical analysis
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
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Summary:As a specific kind of banded matrices, heptadiagonal matrices arise frequently in a variety of fields in theoretical and computational chemistry. In this paper, we present a fast and reliable algorithm for numerically evaluating the determinants of heptadiagonal Toeplitz matrices by a certain type of matrix reordering and partitioning, and linear transformation. In this algorithm, we show that the determinant of an n -by- n heptadiagonal Toeplitz matrix can be implicitly evaluated by computing the determinant of a 6-by-6 matrix which is obtained after the ( n −6)th iteration of linear transformation of a 6-by-3 matrix. The results of some numerical experiments are provided to illustrate the accuracy and efficiency of the proposed algorithm and its competitiveness with Gaussian elimination algorithm and MATLAB built-in function.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-023-01459-7