On a fast and nearly division-free algorithm for the characteristic polynomial

11/25/2020

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by   Fredrik Johansson, et al.

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We review the Preparata-Sarwate algorithm, a simple O(n^3.5) method for computing the characteristic polynomial, determinant and adjugate of an n × n matrix using only ring operations together with exact divisions by small integers. The algorithm is a baby-step giant-step version of the more well-known Faddeev-Leverrier algorithm. We make a few comments about the algorithm and evaluate its performance empirically.