Lebesgue functions and Lebesgue constants in polynomial interpolation

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İBRAHİMOĞLU B. A.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Review
  • Publication Date: 2016
  • Doi Number: 10.1186/s13660-016-1030-3
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: polynomial interpolation, Lebesgue function, Lebesgue constant, LAGRANGE INTERPOLATION, PROJECTION, POINTS
  • Yıldız Technical University Affiliated: Yes

Abstract

The Lebesgue constant is a valuable numerical instrument for linear interpolation because it provides a measure of how close the interpolant of a function is to the best polynomial approximant of the function. Moreover, if the interpolant is computed by using the Lagrange basis, then the Lebesgue constant also expresses the conditioning of the interpolation problem. In addition, many publications have been devoted to the search for optimal interpolation points in the sense that these points lead to a minimal Lebesgue constant for the interpolation problems on the interval .