Interpolatory estimates in monotone piecewise polynomial approximation

D. Leviatan*, I. L. Petrova

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given a monotone function f∈Cr[−1,1], r≥1, we obtain pointwise estimates for its monotone approximation by piecewise polynomials involving the second order modulus of smoothness of f(r). These estimates are interpolatory estimates, namely, the piecewise polynomials interpolate the function at the endpoints of the interval. However, they are valid only for n≥N(f,r). We also show that such estimates are in general invalid with N independent of f.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalJournal of Approximation Theory
Volume223
DOIs
StatePublished - Nov 2017

Keywords

  • Degree of pointwise approximation
  • Jackson-type interpolatory estimates
  • Monotone approximation by piecewise polynomials

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