Displaying similar documents to “The Weierstrass theorem on polynomial approximation”

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

Kyurkchiev, Nikolay, Andreev, Andrey (2013)

Serdica Journal of Computing

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ACM Computing Classification System (1998): G.1.2. Moduli for numerical finding of the polynomial of the best Hausdorff approximation of the functions which differs from zero at just one point or having one jump and partially constant in programming environment MATHEMATICA are proposed. They are tested for practically important functions and the results are graphically illustrated. These moduli can be used for scientific research as well in teaching process of Approximation...

Nearly Coconvex Approximation

Leviatan, D., Shevchuk, I. (2002)

Serdica Mathematical Journal

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* Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001 Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are nearly coconvex with it, namely, polynomials and piecewise polynomials that preserve the convexity of f except perhaps in some small neighborhoods of the points where f changes...

On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

Kyurkchiev, Nikolay, Markov, Svetoslav (2015)

Serdica Journal of Computing

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We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric....

Polynomial approximations and universality

A. Mouze (2010)

Studia Mathematica

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We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results...