Integration of Multivariate Haar Wavelet Series

Authors:
Stefan Heinrich;Fred J. Hickernell;Rong-Xian Yue
Affiliations:
-;-;-
Venue:
WAA '01 Proceedings of the Second International Conference on Wavelet Analysis and Its Applications
Year:
2001

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Abstract

This article considers the error of integrating multivariate Haar wavelet series by quasi-Monte Carlo rules using scrambled digital nets. Both the worst-case and random-case errors are analyzed. It is shown that scrambled net quadrature has optimal order. Moreover, there is a simple formula for the worst-case error.