On finding multiplicities of characteristic polynomial factors of black-box matrices

We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to matrices either over the integers or over a large enough finite field. Experiments show that these methods perform efficiently in practice. Combined in an adaptive strategy, these algorithms reach significant speedups in practice for some integer matrices arising in an application from graph theory. Categories and subject description: G.4 [Mathematics and Computing]: Mathematical Software, Algorithm De

• Type: Conference
• Year: 2009
• Where: ISSAC
• Authors: Jean-Guillaume Dumas, Clément Pernet, B. David Saunders
• Keywords: Characteristic Polynomial, Compute, ISSAC 2009, Mathematics, Minimal Polynomial