Convergence of a class of interpolatory splines for holomorphic functions
The present paper is a follow up to the remarkable paper ''Convergence of complete spline interpolation of holomorphic functions'' by \textit{C. A. Micchelli} and the second author [Ark. Math. 23, 159-170 (1985)]. In the present paper, the authors generalize the interpolation conditions of the earlier paper to \(S^{(v)}(x_ i)=f^{(v)}(x_ i),\) \(v=0,1,...,\alpha_ i-1\), \(i=1,...,\ell\) and \(S^{(v)}(1)=f^{(v)}(1),\) \(v=0,1,...,m+d-1\), \(S^{(v)}(- 1)=f^{(v)}(-1),\) \(v=0,1,...,n-1\). Here \(\alpha_ i\), \(\ell\), m and d are positive integers, and S is a spline of degree \(2m+d-1\) with \(\sum^{\ell}_{i=1}\alpha_ i\) fixed knots. The convergence, as m tends to infinity, of the interpolating splines S(x) is settled.
scientific article; zbMATH DE number 3964614