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

TL;DR

This paper explores weighted Lagrange interpolation with orthogonal polynomials, providing error bounds, a sufficient condition for Stenger's conjecture, and numerical verification to advance understanding of polynomial approximation methods.

Contribution

It introduces a new error estimation bound, a sufficient condition for Stenger's conjecture, and numerical validation within the context of weighted orthogonal polynomial interpolation.

Findings

Established an upper bound for interpolation error.

Provided a numerical verification of Stenger's conjecture.

Proposed a weighted Lagrange interpolation framework using orthogonal polynomials.

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.