A fast elementary algorithm for computing the determinant of toeplitz matrices · arXivDesk
1102.0453Jan 29, 201112 pages. The article is rewritten completely. There are major changes in the title, abstract and references. The results are generalized to any Toeplitz matrix, but the formulas for Pentadiagonal case are still included
A fast elementary algorithm for computing the determinant of toeplitz matrices
In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order k2logn+k3, where n is the number of rows of the Toeplitz matrix and k
Nearby in the stack
is the bandwidth size. This is possible because such a determinant can be expressed as the determinant of certain parts of
n
-th power of a related
k×k
companion matrix. In this paper, we give a new elementary proof of this fact, and provide various examples. We give symbolic formulas for the determinants of Toeplitz matrices in terms of the eigenvalues of the corresponding companion matrices when