Cubic spline interpolation of continuous functions

AbstractLet [0, 1] be partitioned into subintervals h1,…, hn. Let Pn be an associated cubic spline interpolation operator defined on the space C[0, 1]. Let h0 = hnand mn = max{hihj: ¦i − j¦ = 1}. Examples are given for which mn is uniformly bounded as n tends to infinity while ∥Pn∥ is unbounded. The periodic cubic spline interpolation operator is shown to have uniformly bounded norm if mn ⩽ 2.439 for all n