Convergence of a class of interpolatory splines for holomorphic functions
type: Item
instance of: scholarly article
title: Convergence of a class of interpolatory splines for holomorphic functions
zbMATH Open document ID: 0598.41018
DOI: 10.1016/0021-9045(86)90071-7
author: A. Sharma
author: J. Tzimbalario
author: Alfred S. jun. Cavaretta
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 3964614
zbMATH Keywords: interpolation conditions
zbMATH Keywords: interpolating splines
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90071-7
OpenAlex ID: W2140397086
cites work: Q5624248
cites work: Convergence of complete spline interpolation for holomorphic functions
description: scientific article; zbMATH DE number 3964614