The Faddeev-LeVerrier algorithm and the Pfaffian

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 $O(n^{\beta +1})$ where $n$ is the size of the matrix and $O(n^{\beta })$ is the cost of multiplying $n\times n$-matrices, $\beta \in [2,2.37286)$. 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.

15 pages, published version, to appear in Linear Algebra and its Applications

References in corpus (2)

• On a fast and nearly division-free algorithm for the characteristic polynomial
• Characteristic Classes in Computer Algebra

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• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation
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