Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square
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چکیده
منابع مشابه
Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square
We prove new optimal bounds for the error of numerical integration in bivariate Besov spaces with dominating mixed order r. The results essentially improve on the so far best known upper bound achieved by using cubature formulas taking points from a sparse grid. Motivated by Hinrichs’ observation that Hammersley type point sets provide optimal discrepancy estimates in Besov spaces with mixed sm...
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Acknowledgements I would like to express my deepest appreciation to my supervisors Professor Hans-Jürgen Schmeisser and Professor Winfried Sickel for their support and many hints and comments. I thank also Professor Hans Triebel for many valuable discussions on the topic of this work.
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2014
ISSN: 0885-064X
DOI: 10.1016/j.jco.2013.09.001