A method of integration over matrix variables

Integration of Grassmann variables over invariant functions on flat superspaces

We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact expression for the differential operator with respect to the commuting variables which results from Berezin integration over all Grassmann variables. Also, we der...

Iterative Computing over a Unified Relationship Matrix for Information Integration

..................................................................................................I ACKNOWLEDGEMENTS.......................................................................III TABLE OF CONTENTS............................................................................V LIST OF TABLES ..................................................................................... IX LIST OF...

Integration over Spin-Angular Variables in Atomic Physics

A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any oneand two-particle operator for an arbitrary number of shells in an atomic configuration is given. These methods are compared in various aspects, and the advantages or shortcomings of each particular method are discussed. Efficient method to find the abovementio...

A Numerical Integration Method by Using Generalized Series of Functions

A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix

In this paper, a well-conditioned collocation method is constructed for solving general p-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the n...