Spline interpolation on nonunisolvent sets

Spline interpolation is not always a well-posed problem. The interpolation conditions are sufficient to uniquely determine the interpolant only when the nodes are unisolvent. Examples for which this requirement is not fulfilled are the cases of nodes lying in a straight line, circle, plane, sphere a...

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Veröffentlicht in:	IMA journal of numerical analysis 2013-01, Vol.33 (1), p.370-375
1. Verfasser:	Carvalhaes, C. G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Interpolation Numerical analysis Planes Splines Straight lines Well posed problems
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Spline interpolation is not always a well-posed problem. The interpolation conditions are sufficient to uniquely determine the interpolant only when the nodes are unisolvent. Examples for which this requirement is not fulfilled are the cases of nodes lying in a straight line, circle, plane, sphere and other quadratic surfaces. In this paper we revisit this problem and present an approach which naturally extends splines to nonunisolvent sets.
ISSN:	0272-4979 1464-3642
DOI:	10.1093/imanum/drs015