Modified decomposition method for multiple recursive random number generator

This paper considers the problem of generally and efficiently generating random numbers (RNs) for the multiple recursive generators with unrestricted multipliers. A new algorithm based on the decomposition method is proposed. The new algorithm improves the decomposition method in terms of both generality and efficiency. It is shown to be suitable for the signed and unsigned magnitude number systems on a computer, and to require fewer numbers of arithmetic operations than the decomposition method. Several randomly constructed numerical examples illustrate the low variance and efficiency of the new algorithm compared with the decomposition method for various computers.