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

Fredrik Johansson

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arXiv · 2011.12573

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

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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Fredrik Johansson. 2020-11-25. On a fast and nearly division-free algorithm for the characteristic polynomial. https://arxiv.org/abs/2011.12573

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