On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices

In recent years, a number of numerical algorithms of O ( n ) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an n -by- n cyclic pentadiagonal Toeplitz matrix is proposed whose computationa...

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Veröffentlicht in:Journal of mathematical chemistry 2019-09, Vol.57 (8), p.2007-2017
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description In recent years, a number of numerical algorithms of O ( n ) for computing the determinants of cyclic pentadiagonal matrices have been developed. In this paper, a cost-efficient numerical algorithm for the determinant of an n -by- n cyclic pentadiagonal Toeplitz matrix is proposed whose computational cost is estimated at O ( log n ) . The algorithm is based on a structure-preserving matrix factorization and a three-term recurrence relation. We provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and effectiveness of the proposed algorithm, and its competitiveness with other existing algorithms.
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subjects Algorithms
Chemistry
Chemistry and Materials Science
Computer simulation
Determinants
Factorization
Ion migration
Math. Applications in Chemistry
Numerical analysis
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
title On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices
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