Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of arbitrary skew-symmetric matrices that is well suited both for the numeric and symbolic evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90) implementing both methods are given. We also provide simple implementations in Python and Mathematica for purpose of testing, or for exploratory studies of methods that make use of pfaffians.Comment: 13 pages, Download links: http://gamma.ft.uam.es/robledo/Downloads.html and http://www.phys.washington.edu/users/bertsch/computer.htm

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Can Sestamibi kits be prepared with more than the recommended Tc-99m activity? A validation study

Please help populate SUNScholar with the full text of SU research output. Also - should you need this item urgently, please send us the details and we will try to get hold of the full text as quick possible. E-mail to [email protected]. Thank you.Geneeskunde en GesondheidswetenskappeKerngeneeskund