On the best interval quadrature formulae for classes of differentiable periodic functions
نویسندگان
چکیده
In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearrangements of averaged monosplines is proved. © 2007 Elsevier Inc. All rights reserved.
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ورودعنوان ژورنال:
- J. Complexity
دوره 23 شماره
صفحات -
تاریخ انتشار 2007