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Heinrich Richter 《Bl?tter der DGVFM》1979,14(2):359-363
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Dr. Rudolf J. Taschner 《Monatshefte für Mathematik》1981,91(2):139-152
The tool of van der Corput's difference theorem in the theory of uniform distribution is his so-called fundamental inequality.Kemperman showed that even the non-constructive proofs of the difference theorem byBass, Bertrandias andCigler implicitly use a more general form of van der Corput's fundamental inequality. In this article, the inequality which constitutes the basis of the difference theorem will be proved under a very general setting, applications will be demonstrated in connection with the uniform distribution of products of linear forms and a quantitative version of the difference theorem, i. e. an estimation of discrepancies, will be derived. 相似文献
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Ohne Zusammenfassung 相似文献
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Helmut Braß 《Numerische Mathematik》1973,21(5):397-403
Summary LetR
n
[f] be the error of the quadrature formula of Clenshaw and Curtis. Narrow bounds for the coefficientc
n
in |R
n
[f]|c
n
(n!)–1 max |f
(n)
(x)| are given. As a consequence is proven, that the Clenshaw-Curtis-method will generally give more accurate results than the method of Filippi. 相似文献
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