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Quadrature formulas for classes of functions with bounded mixed derivative or difference

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Abstract

Quadrature formulas are considered for classes of smooth functions W rp , B rp , θ with bounded mixed derivative or difference. For the classes of functions indicated above, the result that quadrature formulas constructed with the help of number-theoretic methods are optimal (in the sense of order) is proved, and the optimal order of the error estimates is obtained.

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Author notes

  1. Heping Wang

    Present address: Department of Mathematics, Capital Normal University, 100037, Beijing, China

Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, 100875, Beijing, China

    Heping Wang

Authors
  1. Heping Wang
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Additional information

Project supported by the National Natural Science Foundation of China and the Doctoral Program Foundation of the State Education Commission of China.

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Wang, H. Quadrature formulas for classes of functions with bounded mixed derivative or difference. Sci. China Ser. A-Math. 40, 449–458 (1997). https://doi.org/10.1007/BF02896952

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  • DOI: https://doi.org/10.1007/BF02896952

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