A block diagonalization based algorithm for the determinants of block k-tridiagonal matrices

In the current paper, we present a numerical algorithm for computing the determinants of block k -tridiagonal matrices. The algorithm is based on the use of a fast block diagonalization method and any algorithm for evaluating block tridiagonal determinants. Meanwhile, an explicit numerical formula f...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2021-03, Vol.59 (3), p.745-756
Main Authors: Jia, Ji-Teng, Yan, Yu-Cong, He, Qi
Format: Article
Language:English
Subjects:
Algorithms
Chemistry
Chemistry and Materials Science
Determinants
Math. Applications in Chemistry
Numerical analysis
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
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Summary:In the current paper, we present a numerical algorithm for computing the determinants of block k -tridiagonal matrices. The algorithm is based on the use of a fast block diagonalization method and any algorithm for evaluating block tridiagonal determinants. Meanwhile, an explicit numerical formula for the block k -tridiagonal determinants is also derived, which is based on the combination of the proposed block diagonalization method and a two-term recurrence for block tridiagonal determinants. The experimental results of some representative numerical examples are provided to show the validity and effectiveness of the proposed algorithm and its competitiveness with MATLAB built-in function.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-021-01216-8