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

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.Comment: 6 pages, 1 figure, V2: Minor changes in the text and refs. added, to appear in CP

IBM Online Marketing Strategy

CEMSThis project has been carried out in cooperation between IBM Client Center Moscow and a team of CEMS Students at GSOM. The first part is to do research on where a target group of CIO’s, Chief Engineers and IT Managers are active online and are discussing business pain points, this is done across several industries. The second part is focusing on the development of a strategy, that when implemented, can fulfill IBM Client Centers strategic goals. There is furthermore in this paper included an academic discussion where entrepreneurial frameworks from NOVA courses are discussed and linked to the Business Project. Finally, there is a personal reflection that seeks to improve future team performances

Margit Warburg & Brian Jacobsen (red.): Tørre tal om troen. Religions demografi i det 21. århundrede

Anmeldes af Cecilie Rubow &nbsp