Addendum to: “Rational approximation ofe−xon the positive real axis”

Rational Approximation on the Positive Real Axis

Introduction Rational Chebyshev approximation to reciprocals of certain entire functions by reciprocals of polynomials on the positive real axis has recently attracted the attention of many mathematicians . By developing certain new methods of approach we successfully attacked ([3]-[6]) some of the related problems . This paper is a continuation of our earlier papers ([3]-[6] ) . The results of...

Rational quadratic approximation to real algebraic curves

An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The f...

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...

On a Rational Approximation Problemin the Real Hardy Space

Approximation of hypersingular integral transforms on the real axis

where wα,β(x) = |x|αe−|x| β is a generalized Freud weight with α ≥ 0, β > 1 and 0 ≤ p ∈ N. This topic is of interest, for instance, in the numerical solution of hypersingular integral equations, which are often models for physics and engineering problems (see [5, 2, 4]). To our knowledge, most of the papers available in the literature deal with the approximation of Hadamard integrals on bounded...