Fast parallel computation of characteristic polynomials by Leverrier's power sum method adapted to fields of finite characteristic

  • Arnold Schönhage
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 700)


Symmetric polynomials over F p in n indeterminates x1,..., x n are expressible as rational functions of the first n power sums s j =x l j + ...+ x n j with exponents j not divisible by p. There exist fairly simple regular specializations of these power sums by elements from F p so that all denominators of such rational expressions remain nonzero. This leads to a new class of fast parallel algorithms for the determinant or the characteristic polynomial of n×n matrices over any field of characteristic p with arithmetic circuit depth θ(logn)2.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Arnold Schönhage
    • 1
  1. 1.Institut für Informatik II der Universität BonnBonn 1Germany

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