Local Convergence Of Lagrange Interpolation Associated With Equidistant Nodes

Under the assumption that the function f is bounded on [- 1, 1] and analytic at x = 0 we prove the local convergence of Lagrange interpolating polynomials of f associated with equidistant nodes on [- 1, 1]. The classical results concerning the convergence of such interpolants assume the stronger condition that f 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 f on [- 1, 1].