BEST UNIFORM RATIONAL APPROXIMATION OF xa ON [0, 1]

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

Best Uniform Rational Approximation of x on [0, 1]

For the uniform approximation of xα on [0, 1] by rational functions the following strong error estimate is proved: Let Enn(x, [0, 1]) denote the minimal approximation error in the uniform norm on [0, 1] of rational approximants to xα with numerator and denominator degree at most n, then the the limit lim n→∞ e √ Enn(x , [0, 1]) = 4| sinπα| holds for all α > 0.

Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions

In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class Rn,m of all rational functions of order (n,m) are considered. Let ρn,m = ρn,m( f ; E) be the distance of f in the uniform metric on E from the class Rn,m . We obtain results characterizing the rate of convergence to zero of the sequen...

Best Uniform Rational Approximation of x on [ 0