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Cubic spline interpolation of continuous functions

1974; Elsevier BV; Volume: 10; Issue: 2 Linguagem: Inglês

10.1016/0021-9045(74)90109-9

1096-0430

Martin Marsden,

Approximation Theory and Sequence Spaces

Let [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.