UNIFORM APPROXIMATION BY POLYNOMIAL, RATIONAL AND ANALYTIC FUNCTIONS
نویسندگان
چکیده
منابع مشابه
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.
متن کاملRates 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...
متن کاملBest 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 ...
متن کاملOn Approximation to Analytic Functions by Rational Functions
Let f(z) be analytic in the interior of a rectifiable Jordan curve C and continuous in the corresponding closed region C. The relation between continuity properties of f(z) on C and degree of approximarion to f(z) by polynomials irn(z) in z of respective degrees n, n = 1, 2, • • • , has been extensively studied. In the present paper we study the relation between continuity properties of f(z) on...
متن کاملA 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2008
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972708000464