Computing the invariant structure of integer matrices: fast algorithms into practice

Colton Pauderis, A. Storjohann
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引用次数: 8

Abstract

We present a new heuristic algorithm for computing the determinant of a nonsingular n x n integer matrix. Extensive empirical results from a highly optimized implementation show the running time grows approximately as n3 log n, even for input matrices with a highly nontrivial Smith invariant structure. We extend the algorithm to compute the Hermite form of the input matrix. Both the determinant and Hermite form algorithm certify correctness of the computed results.
计算整数矩阵的不变结构:快速算法的实践
提出了一种计算非奇异n × n整数矩阵行列式的新启发式算法。高度优化实现的大量经验结果表明,即使对于具有高度非平凡Smith不变量结构的输入矩阵,运行时间也大约以n3 log n增长。我们将该算法扩展到计算输入矩阵的Hermite形式。行列式算法和赫米特形式算法证明了计算结果的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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