Abstract: | In the third paper of this series on cardinal spline interpolation 4] Lipow and Schoenberg study the problem of Hermite interpolation . The B-splines are there conspicuous by their absence, although they were found very useful for the case γ = 1 of ordinary (or Lagrange) interpolation (see 5–10]). The purpose of the present paper is to investigate the B-splines for the case of Hermite interpolation (γ > 1). In this sense the present paper is a supplement to 4] and is based on its results. This is done in Part I. Part II is devoted to the special case when we want to solve the problem by quintic spline functions of the class C?(– ∞, ∞). This is the simplest nontrivial example for the general theory. In Part II we derive an explicit solution for the problem (1), where v = 0, 1,…, n. |