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

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Fredrik Johansson
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Abstract

We review the Preparata-Sarwate algorithm, a simple $O(n^{3.5})$ method for computing the characteristic polynomial, determinant and adjugate of an $n \times n$ 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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Dates and versions

hal-03016034 , version 1 (20-11-2020)
hal-03016034 , version 2 (21-11-2020)
hal-03016034 , version 3 (24-11-2020)

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Fredrik Johansson. On a fast and nearly division-free algorithm for the characteristic polynomial. 2020. ⟨hal-03016034v3⟩

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