Random Number Generation

Computational efficient generation of random numbers: Many problems of applied mathematics cannot be solved exactly. But with the help of computer simulations it is often possible to get some further insight. Reliable results in simulation can only be expected if one can go back to efficient and high quality algorithms for the generation of uniformly as well as not uniformly distributed random numbers. Our research is concentrated on: 1. Examination of linear and non-linear congruential generators - with respect to their lattice structure. 2. Suggestions for choosing constants. 3. Developement of efficient algorithms for random number generation. 4. Implementation of our ideas in Win-Rand, a tool for generating random variates coming from a wide range of distributions.