Local support bases for a class of spline functions

J. W. Jerome; L. L. Schumaker

doi:10.1016/0021-9045(76)90092-7

Local support bases for a class of spline functions

J. W. Jerome^*, L. L. Schumaker

^*Corresponding author for this work

Mathematics

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

10 Scopus citations

Abstract

Bases for a class of splines consisting piecewise of elements in the null space of a linear differential operator L with the component pieces tied smoothly together at the knots by requiring the continuity of certain Extended-Hermite-Birkhoff linear functionals are obtained. In particular, first, certain one-sided splines are constructed as linear combinations of an appropriate Green's function, and then local support splines are constructed as linear combinations of the one-sided splines. Finally, local support bases for a finite-dimensional space of splines are obtained.

Original language	English (US)
Pages (from-to)	16-27
Number of pages	12
Journal	Journal of Approximation Theory
Volume	16
Issue number	1
DOIs	https://doi.org/10.1016/0021-9045(76)90092-7
State	Published - Jan 1976

ASJC Scopus subject areas

Analysis
Numerical Analysis
Mathematics(all)
Applied Mathematics

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abstract = "Bases for a class of splines consisting piecewise of elements in the null space of a linear differential operator L with the component pieces tied smoothly together at the knots by requiring the continuity of certain Extended-Hermite-Birkhoff linear functionals are obtained. In particular, first, certain one-sided splines are constructed as linear combinations of an appropriate Green's function, and then local support splines are constructed as linear combinations of the one-sided splines. Finally, local support bases for a finite-dimensional space of splines are obtained.",

author = "Jerome, {J. W.} and Schumaker, {L. L.}",

note = "Funding Information: * Research sponsored in part by the National Science Foundation under Grant GP 32116. + Research sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-74-2598: and in part by the United States Army under Contract No. DA-31-124-ARO-D-462.",

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AU - Jerome, J. W.

AU - Schumaker, L. L.

N1 - Funding Information: * Research sponsored in part by the National Science Foundation under Grant GP 32116. + Research sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-74-2598: and in part by the United States Army under Contract No. DA-31-124-ARO-D-462.

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N2 - Bases for a class of splines consisting piecewise of elements in the null space of a linear differential operator L with the component pieces tied smoothly together at the knots by requiring the continuity of certain Extended-Hermite-Birkhoff linear functionals are obtained. In particular, first, certain one-sided splines are constructed as linear combinations of an appropriate Green's function, and then local support splines are constructed as linear combinations of the one-sided splines. Finally, local support bases for a finite-dimensional space of splines are obtained.

AB - Bases for a class of splines consisting piecewise of elements in the null space of a linear differential operator L with the component pieces tied smoothly together at the knots by requiring the continuity of certain Extended-Hermite-Birkhoff linear functionals are obtained. In particular, first, certain one-sided splines are constructed as linear combinations of an appropriate Green's function, and then local support splines are constructed as linear combinations of the one-sided splines. Finally, local support bases for a finite-dimensional space of splines are obtained.

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Local support bases for a class of spline functions

Abstract

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