On the numerical integration of high-dimensional Walsh-series by Quasi-Monte Carlo methods

Functions which can be represented by rapidly converging Walsh-series play an important role in the theory of signal-processing and image- processing. A special Quasi-Monte Carlo method for the numerical integration of such functions in high dimensions is developed in the present paper. The method is based on the theory of (t, m, s)-nets developed by Niederreiter in the context of irregularities of distribution. Concrete numerical experiments will show the high practical quality of the method.