In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, dσ̂ (t) = (t − z)2 dσ(t), where it is allowed z to be in supp(dσ).Also, we present an application of modified algorithm to the measures dσ̂ (t) = T 2 2 (t) dσ(t) and dσ ′(t) = t2T 2 2 (t) dσ(t), where T2(t) = t2 − 1 2 is the second degree monic Chebyshev polynomial of the first kind and dσ(...

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Padé approximations, linear and nonlinear Padé–...

1 Department of Mathematics, Islamic Azad University, Khorasgan Branch, 81515-158 Isfahan, Iran 2 Department of Mathematics, Khansar Faculty of Computer and Mathematics, University of Isfahan, Isfahan 81746-73441, Iran 3 Department of Physics, Faculty of Science, University PutraMalaysia, 43400 Serdang, Selangor, Malaysia 4 Department of Mathematics, Islamic Azad University, Mobarakeh Branch, 8...

Domain theory has been used with great success in providing a semantic framework for Turing computability, over both discrete and continuous spaces. On the other hand, classical approximation theory provides a rich set of tools for computations over real functions with (mainly) polynomial and rational function approximations. We present a semantic model for computations over real functions base...

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order γ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the soluti...

In this paper we introduce an algorithm for computing nonlinear continuous Chebyshev approximations. The algorithm is based on successive linearizations within adaptively adjusted neighborhoods. The convergence of the algorithm is proven under some general assumptions such that it is applicable for many Chebyshev approximation problems discussed in the literature. It, like the Remez exchange me...

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...