On weighted \((0,2)\)-interpolation on infinite interval \((-\infty,+\infty)\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0972.41003
publication date: 2001-06-12T00:00:00Z
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1603961
zbMATH Keywords: weighted interpolation
zbMATH Keywords: Pal-type interpolation
zbMATH Keywords: Hermite polynomial
MaRDI profile type: Publication
author: S. Datta
author: P. Mathur
title: On weighted \((0,2)\)-interpolation on infinite interval \((-\infty,+\infty)\)
published in: Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica
review text: The paper investigates the Turán-type interpolation problem: to define the polynomial \(R_n\) of lowest possible degree satisfying the conditions NEWLINE\[NEWLINER_n(x_{i,n})=y_{i,n}, \quad (wR_n)^{''}(x_{i,n})=y_{i,n}^{''}, \quad i=1,\dots,n,NEWLINE\]NEWLINE where \(w \in C^2(a,b)\) is a weighted function and \(x_{i,n}\) are some interpolation basic points. The authors prove that taking the roots of the \(n\)-th Hermite polynomal \(H_n(x)\) as nodes, for each positive integer \(n\) there exists such a unique weighted \((0,2)\)-interpolatory polynomial \(R_n\) of degree \(\leq 2n\) satisfying the additional condition \(R_n(0)=y_{0,n}\) if \(n\) is even, and \(R_n^{'}(0)=y_{0,n}^{'}\) if \(n\) is odd.
description: scientific article; zbMATH DE number 1603961