Weighted Discrepancy and High-Dimensional Numerical Integration |
| |
Authors: | G Larcher F Pillichshammer K Scheicher |
| |
Institution: | (1) Institut für Analysis, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria |
| |
Abstract: | The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences. |
| |
Keywords: | Weighted discrepancy numerical integration Koksma– Hlawka inequality Faure– Niederreiter net Sobol– Niederreiter net |
本文献已被 SpringerLink 等数据库收录! |