The method described by D. Braess (J. Approx. Theory 40 (1984), 375-379) is applied to study approximation of ez on a disk rather than an interval. Let E,, be the distance in the supremum norm on Izl <p from e' to the set of rational functions of type (m, n). The analog of Braess' result turns out to be E-m!n!pm+n+l m " (m+n)!(m+n+l)! as m+n+co' This formula was obtained originally for a specia...

The usual way of the implementation of on-line discrete Hilbert transformers is the design of linear phase finite impulse response (FIR) filters. Recently, a method has been published for the design of infinite impulse response (IIR) Hilbert transformers as well. The paper introduces a new method for the design of both FIR and IIR Hilbert transformers, based on a parameter estimation method for...

ECG (Electrocardiogram) signals originating from heart muscles, generate massive volume of digital data. They need to be compressed or approximated for efficient transmission and storage. ECG signal compression is traditionally performed in three ways: direct, transform and parameter extraction. Polynomial approximation which is a form of parameter extraction method, is employed here. This pape...

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

In this paper we compare Krylov subspace methods with Chebyshev series expansion for approximating the matrix exponential operator on large, sparse, symmetric matrices. Experimental results upon negative-definite matrices with very large size, arising from (2D and 3D) FE and FD spatial discretization of linear parabolic PDEs, demonstrate that the Chebyshev method can be an effective alternative...

In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...

ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...

This paper deals with using MATLAB function and tools for designing first-order analogue Chebysev filters and IIR Chebysev filters. The first part of this paper is focused on a design of analogue filter via Chebyshev approximation approach, i. e. features and mathematical background of this iso-extremal approximation, approximation of normalized low-pass (NLP, also NDP in Czech) filter, and mat...

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. Keywords—Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best ...