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arXiv · 2008.04247

The Faddeev-LeVerrier algorithm and the Pfaffian

Christian Baer
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Abstract

We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost $O(n^{β+1})$ where $n$ is the size of the matrix and $O(n^β)$ is the cost of multiplying $n\times n$-matrices, $β\in[2,2.37286)$. We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.

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Christian Baer. 2021-08-05. The Faddeev-LeVerrier algorithm and the Pfaffian. https://doi.org/10.1016/j.laa.2021.07.023

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