Fast Deterministic Computation of Determinants of Dense Matrices (1999)
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| Venue: | IN PROCEEDINGS OF ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION |
| Citations: | 20 - 2 self |
BibTeX
@INPROCEEDINGS{Abbott99fastdeterministic,
author = {John Abbott and Manuel Bronstein and Thom Mulders},
title = {Fast Deterministic Computation of Determinants of Dense Matrices},
booktitle = {IN PROCEEDINGS OF ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION},
year = {1999},
pages = {197--204},
publisher = {ACM Press}
}
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Abstract
In this paper we consider deterministic computation of the exact determinant of a dense matrix M of integers. We present a new algorithm with worst case complexity O \Gamma n 4 (log n + log jjM jj) + n 3 log 2 jjM jj \Delta , where n is the dimension of the matrix and jjM jj is a bound on the entries in M , but with average expected complexity O \Gamma n 4 + n 3 (log n + log jjM jj) 2 \Delta , assuming some plausible properties about the distribution of M . We will also describe a practical version of the algorithm and include timing data to compare this algorithm with existing ones. Our result does not depend on "fast" integer or matrix techniques.
