best polynomial approximation

In this paper, the solution of the general integral equation of the second kind is approximated using polynomials. These polynomials are obtained based on the Remez algorithm and the minimization of residual function. The nature of the use of the Remez algorithm in the proposed method will lead to the conversion of the integral equation to a system of algebraic equations and obtaining the best polynomial approximation for the solution of an integral equation.  Also, the convergence analysis of the approach is discussed. Finally, some numerical examples and comparisons with previous results confirm the efficiency and high accuracy of the presented method.

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

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.