Local Convergence of Lagrange Interpolation Associated with Equidistant Nodes Original Research Article

Under the assumption that the function ƒ is bounded on [−1, 1] and analytic at x = 0 we prove the local convergence of Lagrange interpolating polynomials of ƒ associated with equidistant nodes on [- 1, 1]. The classical results concerning the convergence of such interpolants assume the stronger condition that ƒ is analytic on [−1, 1]. A de Montessus de Ballore type theorem for interpolating rationals associated with equidistant nodes is also established without assuming the global analyticity of ƒ on [−1, 1].