Convergence of spline interpolation processes and conditionality of systems of equations for spline construction

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3 Citations (Scopus)

Abstract

This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the kth derivative in B-splines is equivalent to the problem of convergence of the interpolation process for the Kth spline derivative in the class of functions with continuous Kth derivatives. It is established that for interpolation with splines of degree 2n - 1, the conditions that the projectors corresponding to the derivatives of orders k and 2n - 1 - k be bounded are equivalent. Bibliography: 26 titles.

Original languageEnglish
Pages (from-to)550-564
Number of pages15
JournalSbornik Mathematics
Volume210
Issue number4
DOIs
Publication statusPublished - Apr 2019

Keywords

  • Conditionality
  • Construction algorithms
  • Convergence
  • Interpolation
  • Projector norm
  • Splines
  • construction algorithms
  • convergence
  • projector norm
  • conditionality
  • BAND MATRICES
  • splines
  • INVERSES
  • interpolation
  • NORM

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