Weighted Lagrange Interpolation Using Orthogonal Polynomials: Stenger's Conjecture, Numerical Approach

Abstract

In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error estimation for such kinds of approximations. Later, we introduce the sufficient condition of Stenger's conjecture for orthogonal polynomials and numerical verification for such conjecture.