A factorization algorithm to compute Pfaffians
  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. 
J\"urgen Rubow and Ulli Wolff
hep-lat cond-mat.stat-mech math.NA