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

MG de Bruin

doi:10.1016/j.cam.2004.09.035

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

MG de Bruin

Research output: Contribution to journal › Article › Scientific › peer-review

6 Citations (Scopus)

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

Original language	Undefined/Unknown
Pages (from-to)	175-184
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	179
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cam.2004.09.035
Publication status	Published - 2005

Keywords

academic journal papers
ZX CWTS JFIS < 1.00

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10.1016/j.cam.2004.09.035

Cite this

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abstract = "In (simple) P{\'a}l-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: P{\'a}l-type interpolation; Regularity",

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AB - 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

KW - academic journal papers

KW - ZX CWTS JFIS < 1.00

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