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Efficient Computation of the Characteristic Polynomial by Jean-Guillaume Dumas; Clément Pernet; Zhendong Wan is a scholarly article available to read on EtoBox.

What is Efficient Computation of the Characteristic Polynomial about?

We deal with the computation of the characteristic polynomial of dense matrices over word size finite fields and over the integers. We first present two algorithms for finite fields: one is based on Krylov iterates and Gaussian elimination. We compare it to an improvement of the second algorithm of Keller-Gehrig. Then we show that a generalization of Keller-Gehrig's third algorithm could improve both complexity and computational time. We use these results as a basis for the computation of the characteristic polynomial of integer matrices. We first use early termination and Chinese remaindering for dense matrices. Then a probabilistic approach, based on integer minimal polynomial and Hensel factorization, is particularly well suited to sparse and/or structured matrices.

Author

Jean-Guillaume Dumas; Clément Pernet; Zhendong Wan

Publisher

ACM

Published

2005

Language

EN