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

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 cycl...

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Bibliographic Details
Published in:Numerical algorithms 2016-02, Vol.71 (2), p.337-348
Main Authors: Jia, Ji-Teng, Li, Su-Mei
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computation
Computer Science
Determinants
Mathematical models
Matrix partitioning
Numeric Computing
Numerical Analysis
Original Paper
Partitions
Theory of Computation
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Summary: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 7 n + 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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-015-9995-4