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On the Application of the Peano Representation of Linear Functionals in Numerical Analysis

  • Helmut Brass
  • Klaus-Jürgen Förster
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

For more than 80 years, Peano kernel theory has proven to be an important tool in numerical analysis. It is one aim of this paper to elucidate the wide range of possible applications of Peano’s representation of linear functionals. In the literature, Peano kernel theory is mostly considered for restricted classes of linear functionals. In this paper, it is also our objective to give an elementary but general approach for continuous linear functionals on C[a, b].

Key words and phrases

Peano kernel theory Inequalities for linear functionals Error estimates Quadrature Interpolation Optimal formulas 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Helmut Brass
    • 1
  • Klaus-Jürgen Förster
    • 2
  1. 1.Institut für Angewandte MathematikTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Institut für MathematikUniversität HildesheimHildesheimGermany

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