Generalized Haar Function Systems, Digital Nets and Quasi-monte Carlo Integration

SPIE 2762, and is made available as an electronic reprint with permission of SPIE. Single print or electronic copies for personal use only are allowed. Systematic or multiple reproduction, or distribution to multiple locations through an electronic listserver or other electronic means, or duplication of any material in this paper for a fee or for commercial purposes is prohibited. By choosing to view or print this document, you agree to all the provisions of the copyright law protecting it. ABSTRACT Quasi-Monte Carlo methods are an extremely eeective approach for computing high dimensional integrals. In this paper we present a concept based on generalized Haar functions systems that allows to estimate the integration error for practically relevant classes of functions. The local structure of the Haar functions yields interesting new aspects in proofs and results. The results are supplemented by concrete computer calculations.