Computing the determinant of pentadiagonal toeplitz matrices in logarithmic time

Details Computing the determinant of pentadiagonal toeplitz matrices in logarithmic time Computing the determinant of pentadiagonal toeplitz matrices in logarithmic time

2011-01-29

arxiv.org/abs/1102.0453v1

Mathematics

Numerical Analysis

9 pages

Scientific paper

In recent years, a number of fast algorithms for computing the determinant of a pentadiagonal Toeplitz matrix were developed. Previous algorithms require at least $O(\sqrt{n})$ operations to compute the determinant of such matrices of size $n \times n$. In this paper, we give a new algorithm requiring $O(\log{n})$ operations. Moreover, we give formulas for the determinant of a pentadiagonal Toeplitz matrix in terms of the roots of a degree 4 monic polynomial with coefficients obtained from the nonzero entries of the Toeplitz matrix.

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