Continuity of best reciprocal polynomial approximation on [0, ∞)

Continuity Properties of Best Analytic Approximation

Let A be the operator which assigns to each m×n matrix-valued function on the unit circle with entries in H∞+C its unique superoptimal approximant in the space of bounded analytic m × n matrix-valued functions in the open unit disc. We study the continuity of A with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, A is continuous at any f...

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.

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...

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.

Best Uniform Rational Approximation of x on [ 0