Gridification of the Solution of highdimensional improper Integration and Integral Equations

The scope of the paper is the development of new methods for high dimensional numerical integration of unbounded functions, the solution of integral equations and the direct search for good lattice points in a grid environment. From the mathematical point of view we use the Zinterhof sequences for the removal of singularities by means of certain integral transforms. The algorithms for numerical integration (by summation and convolution) and a brute force search for good integration numbers have been parallelized for use in the grid environment. We also show the high suitability of novel computing machinery, such as the STI Cell processor and CUDA-enabled devices (NVIDIA GPUs) for these tasks. 1. The mathematical Methods 1.1. Numerical Integration Methods avoiding the Curse of Dimensionality Consider any classical integration method