Berkowitz's Algorithm and Clow Sequences
Rings and Algebras
2007-05-23 v1
Abstract
We present a combinatorial interpretation of Berkowitz's algorithm. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the computations performed by Berkowitz's algorithm, which otherwise is quite difficult to analyze. The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences.
Keywords
Cite
@article{arxiv.math/0201315,
title = {Berkowitz's Algorithm and Clow Sequences},
author = {Michael Soltys},
journal= {arXiv preprint arXiv:math/0201315},
year = {2007}
}
Comments
Submitted to ELA (Electronic Journal of Linear Algebra)