منابع مشابه
Interpolation Polynomials of Bernstein Types: A Review
School of Science, Dalian Nationalities University Dalian 116600, Liaoning, P.R. China Abstract In this work, we mainly review two methods for improving the uniform convergence of the known Lagrange interpolation polynomial put forward by Bernstein, namely, the method of weighted mean for basic functions of interpolation and the method of lowering some interpolation conditions. Moreover, we pre...
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The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so–called Bernstein–Bézier form of a polynomial.
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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]...
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We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.
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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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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1954
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1954-09804-x