The Multiple-Recursive Matrix Method for Pseudorandom Number Generation

We carry out an in-depth analysis of the multiple-recursive matrix method for uniform pseudorandom number generation which was introduced in an earlier paper of the author. This method yields much larger period lengths than the GFSR method with the same order of the recursion and the same precision. Besides periodicity properties, we establish also uniformity properties of s-tuples of successive pseudorandom numbers generated by the multiple-recursive matrix method and we study the performance under the s-dimensional serial test. The uniformity properties and the behavior under the serial test depend on an appropriate figure of merit in the case where the dimension s exceeds the order of the recursion.