منابع مشابه
Bernstein Polynomials and Brownian Motion
One of the greatest pleasures in mathematics is the surprising connections that often appear between apparently disconnected ideas and theories. Some particularly striking instances exist in the interaction between probability theory and analysis. One of the simplest is the elegant proof of the Weierstrass approximation theorem by S. Bernstein [2]: on the surface, this states that if f : [0, 1]...
متن کاملBernstein polynomials and learning theory
When learning processes depend on samples but not on the order of the information in the sample, then the Bernoulli distribution is relevant and Bernstein polynomials enter into the analysis. We derive estimates of the approximation of the entropy function x log x that are sharper than the bounds from Voronovskaja’s theorem. In this way we get the correct asymptotics for the Kullback-Leibler di...
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This article has no abstract.
متن کاملMultivariate Bernstein polynomials and convexity
It is well known that in two or more variables Bernstein polynomi-als do not preserve convexity. Here we introduce two variations, one stronger than the classical notion, the other one weaker, which are preserved. Moreover, a weaker suucient condition for the monotony of subsequent Bernstein polynomials is given. linearly independent, in the course of which d has to be greater than or equal to ...
متن کاملLocal Derivatives and Bernstein Polynomials
We introduce the local derivatives of a Weyl algebra and prove a theorem of I. N. Bernstein concerning the existence of certain polynomials relating to the action of local derivatives.
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2006
ISSN: 0002-9890
DOI: 10.2307/27642086