Uniform rational approximation with osculatory interpolation

On the Osculatory Rational Interpolation Problem

The problem of the existence and construction of a table of osculating rational functins fj m for 1, m > 0 is considered. First, a survey is given of some results from the theory of osculatory rational interpolation of order s¡ — 1 at points x¡ for i > 0. Using these results, we prove the existence of continued fractions of the form c0 + c, -(x y0) + . . . + ck-(x y0) . . . (x yk_x) ck + l •<* ...

Bivariate Blending Thiele-Werner’s Osculatory Rational Interpolation

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...

Error formulas for multivariate rational interpolation and Pad6 approximation

The univariate error formulas for Pad6 approximants and rational interpolants, which are repeated in Section 2, are generalized to the multivariate case in Section 4. We deal with "general order" multivariate Pad~ approximants and rational interpolants, where the numerator and denominator polynomials as well as the equations expressing the approximation order, can be chosen by the user of these...