Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces

Multi-Version Program Analysis

计算机科学;物理学

Michael Gnewuch

Others  :  http://drops.dagstuhl.de/opus/volltexte/2009/2296/pdf/09391.GnewuchMichael.Paper.2296.pdf
PID  :  6409

学科分类：计算机科学（综合）

来源: CEUR

【 摘 要 】

We extend the notion of L_2 B discrepancy provided in [E. Novak, H. Woz´niakowski, L_2 discrepancy and multivariate integration, in: Analytic number theory. Essays in honour of Klaus Roth. W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt, and R. C. Vaughan (Eds.), Cambridge University Press, Cambridge, 2009, 359 – 388] to the weighted L_2 B discrepancy. This newly defined notion allows to consider weights, but also volume measures different from the Lebesgue measure and classes of test sets different from measurable subsets of some Euclidean space. We relate the weighted L_2 B discrepancy to numerical integration defined over weighted reproducing kernel Hilbert spaces and settle in this way an open problem posed by Novak and Wo´zniakowski.