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Is there a "gold" standard for computing the characteristic polynomial of a given $n \times n$ matrix in finite precision arithmetic on a computer?

There are fast methods running in $O(n^3)$ or even $O(n^\omega)$ :

These algorithms are quite fast but were developed for finite fields and require randomness and matrix inversion, which in finite precision arithmetic can cause numerical problems.

On the other hand there is the Faddeev-Leverrier algorithm which only requires matrix multiplication but runs in time $O(n^4)$.

Does anyone have experience using these algorithms for numerical calculations?

Nicolás Quesada
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  • Note that finite precision arithmetic and working in finite field $\mathbb F_{2^n}$ is roughly equivalent since real numbers on computer are stored under the form $x=M.2^{-n}$, this is why these algorithms were developed for finite fields. – zwim May 24 '19 at 22:38
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    Linked. – Cosmas Zachos Jun 09 '21 at 21:53

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