Lacunary Polynomial Spline Interpolation

Lacunary Polynomial Spline Interpolation

A special form of the Birkhoff interpolation problem is investigated. We prove an existence theorem for certain types of interpolation which, in a particular case, reduces to a theorem of Meir and Sharma for (0, 2) interpolation by C3piecewise quintics. The method of proof enables us to obtain L∞-es...

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Veröffentlicht in:SIAM journal on numerical analysis 1976-06, Vol.13 (3), p.369-381
1. Verfasser: Demko, Stephen
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Degrees of polynomials
Error bounds
Existence theorems
Integers
Interpolation
Mathematical functions
Polynomials
Uniqueness
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Zusammenfassung:A special form of the Birkhoff interpolation problem is investigated. We prove an existence theorem for certain types of interpolation which, in a particular case, reduces to a theorem of Meir and Sharma for (0, 2) interpolation by C3piecewise quintics. The method of proof enables us to obtain L∞-estimates for the error in interpolating smooth functions. These error bounds are shown to be sharp by means of a Baire category argument.
ISSN:0036-1429
1095-7170
DOI:10.1137/0713033