Uniform Approximation

Uniform Approximation

 

a type of approximation of a function. In uniform approximation, the “distance” on a given set between the given function f(x) and the approximating function P(x) is measured by the least upper bound of the absolute value of their difference. For example, the distance between the continuous function P(x) and the continuous function f(x) on the closed interval [a, b] is

Uniform approximation is also referred to as Chebyshev approximation, in honor of P. L. Chebyshev, who studied it in 1854. (SeeAPPROXIMATION AND INTERPOLATION OF FUNCTIONS.)

References in periodicals archive ?
Their topics include the degree of uniform approximation by generalized discrete singular operators, Voronovskaya-like asymptotic expansion for generalized discrete singular operators, global smoothness preservation and simultaneous approximation by generalized discrete singular operators, the degree of Lp approximation for multivariate generalized discrete singular operators, and the degree of approximation by multivariate complex generalized discrete singular operators.
The Carleman's theorem is a pointwise approximation result which generalizes the Weierstrass result on uniform approximation by polynomials in compact intervals, since on any compact subinterval of R, the entire function can in turn be approximated uniformly by polynomials, more exactly by the partial sums of is power series (see Remark 2.
In [4], the optimal piecewise uniform quantizer for that source geometry has been designed assuming four cases for the piecewise uniform approximation of the input radius PDF.
Similar to [9], we consider an alternative approach based on the use of polynomials of best uniform approximation to the function 1/[lambda].
It is probably impossible to generate a uniform approximation within the limits of a linear model in the whole interval [0; 40] because periodic functions [f.
Key words and phrases : Sampling series, uniform approximation, reconstruction process, sampling-based signal processing, system representation
Theorem 1 confirms a conjecture of Bagby and Gauthier [5] concerning the relationship between Carleman pairs and pairs for which uniform approximation is possible.
Dovgoshei [2] considered the uniform approximation on compact subsets of the complex plane.
For the applications we have in mind, a rational uniform approximation with an error of [10.
Totik, Uniform approximation by Bernstein-type operators, Indag.

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