A factorization algorithm to compute Pfaffians
J\"urgen Rubow, Ulli Wolff
TL;DR
This paper introduces an explicit factorization algorithm for even antisymmetric matrices, enabling efficient computation of Pfaffians with a cubic time complexity, including their signs.
Contribution
The paper presents a novel factorization method for antisymmetric matrices that simplifies and accelerates Pfaffian calculations compared to previous approaches.
Findings
Efficient N^3/3 flop algorithm for Pfaffian computation
Explicit factorization of even antisymmetric matrices
Accurate determination of Pfaffian signs
Abstract
We describe an explicit algorithm to factorize an even antisymmetric N^2 matrix into triangular and trivial factors. This allows for a straight forward computation of Pfaffians (including their signs) at the cost of N^3/3 flops.
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