Interpolation by splines satisfying mixed boundary conditions

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19 Scopus citations

Abstract

We consider interpolation of Hermite data by splines of degree n with k given knots, satisfying boundary conditions which may involve derivatives at both end points (e.g., a periodicity condition). It is shown that, for a certain class of boundary conditions, a necessary and sufficient condition for the existence of a unique solution is that the data points and knots interlace properly and that there does not exist a polynomial solution of degree n-k. The method of proof is to show that any spline interpolating zero data vanishes identically, rather than the usual determinantal approach.

Original languageEnglish
Pages (from-to)369-381
Number of pages13
JournalIsrael Journal of Mathematics
Volume19
Issue number4
DOIs
StatePublished - 1 Dec 1974
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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