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

Fredrik Johansson 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03016034
Contributor : Fredrik Johansson <>
Submitted on : Tuesday, November 24, 2020 - 3:40:53 PM
Last modification on : Thursday, November 26, 2020 - 3:30:18 AM

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  • HAL Id : hal-03016034, version 3
  • ARXIV : 2011.12573

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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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