Abstract
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.
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