学术报告与学术会议

Dany Leviatan教授受邀进行讲座

发布时间: 2019-02-17 20:53:00

题      目:INTERPOLATORY POINTWISE ESTIMATES FOR MONOTONE AND CONVEX PIECEWISE-POLYNOMIAL APPROXIMATION

报 告 人:Dany Leviatan 教授    Tel Aviv University

时      间:2019-02-15 10:30--11:30

地      点:交叉学院108室

报告人简介:

        Dany Leviatan教授是国际著名逼近论专家,在国际发表上百篇学术文章,担任多本著名数学杂志的编辑,曾任以色列特拉维夫大学数学系的系主任和特拉维夫大学的校长(rector)。

摘      要:

        Given a monotone or convex function f, we obtain pointwise estimates for its monotone,respectively, convex approximation by piecewise polynomials involving the second order modulus of smoothness of f^r. These estimates are interpolatory estimates, namely, the piecewise polynomials interpolate the function at the end-points of the interval. However,they are valid only for n > N(f,r). We also show thatsuch estimates are in general invalid with N independent of f. Note that the above estimate in the case r = 0 is achieved by piecewise linears interpolating f at the Chebyshev nodes. This was proved in the early 1980's by DeVore and Yu (for monotone approximation) and by Leviatan (for convex approximation).


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