On a fast and nearly division-free algorithm for the characteristic polynomial
Résumé
We review the Preparata-Sarwate algorithm, a simple O(n3.5) 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.
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