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Numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure

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Abstract

Very recently, an efficient computational algorithm (DETQPT algorithm) for the determinant evaluation of general cyclic pentadiagonal Toeplitz matrices has been proposed by Y.L. Jiang and J.T. Jia (J. Math. Chem. 51: 2503-2513, 2013). In this paper, an explicit formula for the determinant of a cyclic pentadiagonal Toeplitz matrix is derived at first. Then, we present a more efficient numerical algorithm with the cost of \(7n+O(\log \ n)\) for evaluating n-th order cyclic pentadiagonal Toeplitz determinants. The algorithm is based on the use of a certain type of matrix reordering and matrix partition, and equalities involving the products of special kind of relevant matrices. Three numerical examples demonstrate the performance and effectiveness of the proposed algorithm and its competitiveness with other already existing algorithms.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Ji-Teng Jia & Su-Mei Li

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  1. Ji-Teng Jia
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  2. Su-Mei Li
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Correspondence to Ji-Teng Jia.

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Jia, JT., Li, SM. Numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure. Numer Algor 71, 337–348 (2016). https://doi.org/10.1007/s11075-015-9995-4

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  • DOI: https://doi.org/10.1007/s11075-015-9995-4

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