Abstract
Quite recently Sloan and Woźniakowski (J. Complexity 14 (1998) 1) introduced a new notion of discrepancy, the so-called weighted L p discrepancy of points in the d-dimensional unit cube for a sequence γ=( γ 1, γ 2,…) of weights. In this paper we prove a nice formula for the weighted L p discrepancy for even p. We use this formula to derive an upper bound for the average weighted L p discrepancy. This bound enables us to give conditions on the sequence of weights γ such that there exists N points in [0,1) d for which the weighted L p discrepancy is uniformly bounded in d and goes to zero polynomially in N −1. Finally we use these facts to generalize some results from Sloan and Woźniakowski (1998) on (strong) QMC-tractability of integration in weighted Sobolev spaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
