An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices (Q765279)

The author presents a new kind of elementary algorithm for computing the determinants of pentadiagonal Toeplitz matrices of order \(n\). This algorithm requires \(56\dot\lfloor\frac{n-4}k\rfloor+30k+O(\log n)\) operations, where \(k\geq 4\) is an integer chosen freely at the beginning of the algorithm. Another main result of this paper gives a fast algorithm for determining when the determinants of pentadiagonal Toeplitz matrices with rational entries are nonzero.