Cubature formulas for function spaces with moderate smoothness
نویسندگان
چکیده
منابع مشابه
Cubature formulas for function spaces with moderate smoothness
We construct simple algorithms for high-dimensional numerical integration of function classes with moderate smoothness. These classes consist of square-integrable functions over the d-dimensional unit cube whose coefficients with respect to certain multiwavelet expansions decay rapidly. Such a class contains discontinuous functions on the one hand and, for the right choice of parameters, the qu...
متن کاملFunction spaces with dominating mixed smoothness
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.
متن کاملOptimal 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...
متن کاملError Estimates for Polyharmonic Cubature Formulas
In the present article we shall present basic features of a polyharmonic cubature formula of degree s and corresponding error estimates. Main results are Markov-type error estimates for differentiable functions and error estimates for functions f which possess an analytic extension to a sufficiently large ball in the complex space Cd . 2000 AMS subject classification: 65D30, 32A35
متن کاملAn encyclopaedia of cubature formulas
About 13 years ago we started collecting published cubature formulas for the approximation of multivariate integrals over some standard regions. In this paper we describe how we make this information available to a larger audience via the World Wide Web.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2007
ISSN: 0885-064X
DOI: 10.1016/j.jco.2007.07.002