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CORR
2007
Springer

Computing Minimal Polynomials of Matrices

13 years 3 months ago
Computing Minimal Polynomials of Matrices
We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an n × n matrix over a finite field that requires O(n3 ) field operations and O(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We compare features of the algorithm with several other algorithms in the literature. In addition we present a deterministic verification procedure which is similarly efficient in most cases but has a worst-case complexity of O(n4 ). Finally, we report the results of practical experiments with an implementation of our algorithms in comparison with the current algorithms in the GAP library.
Max Neunhöffer, Cheryl E. Praeger
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CORR
Authors Max Neunhöffer, Cheryl E. Praeger
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