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

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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-03016034
Contributor : Fredrik Johansson Connect in order to contact the contributor
Submitted on : Tuesday, November 24, 2020 - 3:40:53 PM
Last modification on : Friday, December 3, 2021 - 12:20:06 PM

### Files

paper.pdf
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### Identifiers

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

### Citation

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

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