Generalised Chebyshev polynomials and their use in numerical approximation

Approximation of ECG Signals using Chebyshev Polynomials

The ECG (Electrocardiogram) signal represents electrical activity of heart and is recorded for monitoring and diagnostic purpose. These signals are corrupted by artifacts during acquisition and transmission predominantly by high frequency noise due to power line interference, electrode movements, etc. Addition of these noise change the amplitude and shape of the ECG signal which affect accurate...

Numerical Chebyshev Approximation by Interpolating Rationals

The paper is concerned with the Chebyshev approximation of decay-type functions /(x) by interpolating rationals. The interpolating points are chosen to be the zeros of j(x). Existence, uniqueness and characterization of best approximations are first shown. An exchange algorithm is then described for computing the best approximation.

Legendre polynomials Triple Product Integral and lower-degree approximation of polynomials using Chebyshev polynomials

In this report, we present two mathematical results which can be useful in a variety of settings. First, we present an analysis of Legendre polynomials triple product integral. Such integrals arise whenever two functions are multiplied, with both the operands and the result represented in the Legendre polynomial basis. We derive a recurrence relation to calculate these integrals analytically. W...

Chebyshev Polynomials in the Numerical Solution of Differential Equations

Amongst satisfactory techniques for the numerical solution of differential equations, the use of Chebyshev series is often avoided because of the tedious nature of the calculations. A systematic application of the Chebyshev method is given for certain fourth order boundary value problems in which the derivatives have polynomial coefficients. Numerical results for various problems using the Cheb...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules