(0,m) Pál-type interpolation: interchanging value- and derivative-nodes

Journal article (2005)

Authors

MG de Bruin Old - EWI Ch. Classical Analysis
Research Group
Old - EWI Ch. Classical Analysis
More Info
expand_more

Published Date

2005

Language

Undefined/Unknown

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Research Group

Old - EWI Ch. Classical Analysis

Abstract

In (simple) Pál-type interpolation the problem consists of finding a polynomial of degree n+m-1 that has prescribed values at, say, n pairwise distinct points and prescribed values for the rth derivative r1 at (another) set of m distinct points.

The problem is named regular if it has a unique solution for any set of data; this is equivalent to the homogeneous problem (all prescribed values are 0) having the trivial solution only.

In this paper the effect of interchanging the value-nodes and the derivative-nodes on the regularity of the problem is studied for several sets of nodes.

Keywords: Pál-type interpolation; Regularity