Efficient mixed rational and polynomial approximation of matrix functions

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.

On the Convergence of Polynomial Approximation of Rational Functions

This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r_r matrix are less than 2, where r is the degree of the rational function (or curve), and where the e...

Best uniform polynomial approximation of some rational functions

This thesis is based on the following paper :Mehdi Dehghan , M.R. Eslahchi, Best uniform polynomialapproximation of some rational functions , Computers andMathematics with Applications ,Best polynomial approximation problem is one of the mostimportant and applicable subjects in the approxi References1. [1] J . C . Mason , D . C . Handscomb , Chebyshevpolynomials ...

Polynomial Approximation of Functions

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...

Approximation by Rational Functions