Piecewise L-splines of order 4: Interpolation and L2 error bounds for splines in tension

Ziv Ayalon*, Nira Dyn, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

PiecewiseL -splines are generalizations of L-splines, in the sense that they satisfy different differential equations in different mesh intervals. Prenter attempted in [P.M. Prenter, Piecewise L-Splines, Numer. Math. 18 (2) (1971) 243-253] to obtain results on piecewise L-splines by generalizing the results of Schultz and Varga on L-splines in [M.H. Schultz, R.S. Varga, L-Splines, Numer. Math. 10 (1967) 345-369]. We show that the results of Prenter are erroneous, and provide correct ones for piecewise L-splines of order 4. We prove the existence and uniqueness of such interpolants and establish the first and second integral relations. In addition we obtain new L2 error bounds for the special case of splines in tension with variable tension parameters.

Original languageEnglish
Pages (from-to)421-431
Number of pages11
JournalJournal of Approximation Theory
Volume161
Issue number2
DOIs
StatePublished - Dec 2009

Keywords

  • Exponential splines
  • Interpolation
  • L error bounds
  • Piecewise L-splines
  • Splines in tension

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