Generalized monosplines and optimal approximation

Research output: Contribution to journalArticlepeer-review

Abstract

Generalized monosplines of least norm are shown to exist and to determine optimal approximation processes such as numerical integration, interpolation and best approximating spaces. This extends various classical results related to monosplines and perfect splines, which are particular cases of generalized monosplines. The analysis here also provides for a unified treatment of the two classical classes of monosplines and perfect splines of least norm, and of their extremal properties.

Original languageEnglish
Pages (from-to)137-154
Number of pages18
JournalConstructive Approximation
Volume1
Issue number1
DOIs
StatePublished - Dec 1985

Keywords

  • AMS classification: 41A15, 41A5, 41A65
  • Extended totally positive kernels
  • Monosplines
  • Monotone norms
  • N-widths
  • Optimal interpolation
  • Optimal quadrature formulas
  • Optimal spaces
  • Perfect splines

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