Journal ArticleDOI
How close is the approximation by Bernstein polynomials
TLDR
Weierstrass as discussed by the authors showed that any continuous function can be uniformly approximated by polynomials on a bounded, closed real interval, and this theorem can be generalized to continuous functions.Abstract:
A famous theorem of Weierstrass, dating from 1885, states that any continuous function can be uniformly approximated by polynomials on a bounded, closed real interval.read more
Citations
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Journal ArticleDOI
The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)
TL;DR: A Glimpse at Set Theory: The Topology of Cartesian Spaces and the Functions of One Variable.
Journal ArticleDOI
Approximating Lipschitz and continuous functions by polynomials; Jackson’s theorem
TL;DR: The celebrated Weierstrass theorem of 1885 states that continuous functions can be uniformly approximated by polynomials on any bounded, closed interval as mentioned in this paper . But how well can we approximate continuous functions with a certain degree?
References
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Book
Introduction to approximation theory
TL;DR: In this paper, Tchebycheff polynomials and other linear families have been used for approximating least-squares approximations to systems of equations with one unknown solution.
Journal ArticleDOI
The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)
TL;DR: A Glimpse at Set Theory: The Topology of Cartesian Spaces and the Functions of One Variable.
Book
The Elements of Real Analysis
TL;DR: A Glimpse at Set Theory The Real Numbers The Topology of Cartesian Spaces as discussed by the authors The set theory of set theory is based on Cartesian spaces and functions of one variable.
Journal ArticleDOI
Monotonicity of weighted averages of convex functions
TL;DR: In this paper, the authors consider weighted averages of the form Bn(W, f ) = ∑r=0 wn,r f (r/n), where W is a summability matrix and f is convex.