Faster algorithms for the characteristic polynomial
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast computation of power series solutions of systems of differential equations
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic normal forms and dynamic characteristic polynomial
Theoretical Computer Science
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A deterministic algorithm for computing the Frobenius canonical-form of a matrix over a field is described. A similarity transformation-matrix is recovered in the same time. The algorithm is nearly optimal, requiring about the same number of field operations as required for matrix multipication. Previously-known reductions to matrix multiplication are probabilistic.