this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

The aim of this paper is to study the Lagrange multivariate interpolation problems in the space of polynomials of w-degree n. Some new results concerning the polynomial spaces of w-degree n are given. An algorithm for obtaining the w-minimal interpolation space is presented. Key–Words: Lagrange multivariate polynomial interpolation, whomogeneous polynomial spaces, Generalize degree.

8 In his paper " Lagrange interpolation on Chebyshev points of two variables " (J. 9 220–238), Y. Xu proposed a set of Chebyshev like points for polynomial interpolation in the square 10 [−1, 1] 2 , and derived a compact form of the corresponding Lagrange interpolation formula. We inves-11 tigate computational aspects of the Xu polynomial interpolation formula like numerical stability and 12 ef...

Minimal degree interpolation spaces with respect to a nite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solv-able and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange inter...

A lower set of nodes is a subset of a grid that can be indexed by a lower set of indices. In order to apply the Lagrange interpolation formula, it is convenient to express the Lagrange fundamental polynomials as sums of few terms. We present such a formula for the Lagrange interpolation formula in two variables. In the general multidimensional case, we express the Lagrange fundamental polynomia...

In this note we prove mean convergence of Lagrange interpolation at the zeros para-orthogonal polynomials for measures on unit circle which do not belong to Szegő’s class. When measure is in class, proved functions disk algebra.