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

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Abstract

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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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, China

    Ji-Teng Jia

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  1. Ji-Teng Jia
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Correspondence to Ji-Teng Jia.

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This work was supported by the Natural Science Foundation of China (NSFC) under grant 11601408, and the Fundamental Research Funds for the Central Universities under grant JB180706.

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Jia, JT. On a structure-preserving matrix factorization for the determinants of cyclic pentadiagonal Toeplitz matrices. J Math Chem 57, 2007–2017 (2019). https://doi.org/10.1007/s10910-019-01053-w

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  • DOI: https://doi.org/10.1007/s10910-019-01053-w

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