Best Simultaneous Approximation (Chebyshev Centers)

  • Dan Amir
Chapter
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 72)

Abstract

The problem of approximating simultaneously a set of data in a given metric space by a single element of an approximating family arises naturally in many practical problems. A common procedure is to choose the “best” approximant by a least squares principle, which has the advantages of existence, uniqueness, stability and easy computability. However, in many cases the least deviation principle makes more sense. Geometrically, this amounts to covering the given data set by a ball of minimal radius among those centered at points of the approximating family. The theory of best simultaneous approximants in this sense, called also Chebyshev centers, was initiated by A. L. Garkavi about twenty years ago. It has drawn more attention in the last decade, but is still in a developing stage. In this short survey I try to describe the main known results and to point at some of the connections between the theory of Chebyshev centers and other problems of Approximation Theory and of Banach Space Theory.

Keywords

Simultaneous Approximation Normed Linear Space Minimal Projection Asymptotic Center Maximal Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Basel AG 1984

Authors and Affiliations

  • Dan Amir
    • 1
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel-AvivIsrael

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