A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices
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In this paper, we present a new breakdown-free recursive algorithm for computing the determinants of periodic tridiagonal matrices via a three-term recurrence. Even though the algorithm is not a symbolic algorithm, it never suffers from breakdown. Furthermore, the proposed algorithm theoretically produces exact values for periodic tridiagonal matrices whose entries are all given in integer. In addition, an explicit formula for the determinant of the periodic tridiagonal matrix with Toeplitz structure is also discussed.
KeywordsTridiagonal matrices Periodic tridiagonal matrices Determinants Breakdown-free algorithm Three-term recurrence
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The author would like to thank the anonymous referees for valuable comments and suggestions that substantially enhanced the quality of the manuscript.
This work was supported by the National Natural Science Foundation of China (NSFC) under grant no. 11601408, the Natural Science Basic Research Plan in Shaanxi Province of China under grant no. 2017JQ1004, and the Fundamental Research Funds for the Central Universities under grant no. JB180706.
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