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Approximation Theory

  1. Annie Cuyt

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse017

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Cuyt, A. 2009. Approximation Theory. Wiley Encyclopedia of Computer Science and Engineering. 163–171.

Author Information

  1. University of Antwerpen, Department of Mathematics and Computer Science, Antwerpen, Belgium

Publication History

  1. Published Online: 16 MAR 2009

Abstract

In approximation theory, one distinguishes between interpolation and so-called least-squares problems. In the former, one wants the approximate model to take exactly the same values as prescribed by given data at some argument values. In the latter, a set of data is regarded as a trend and is approximated by a simple model in the best sense. The difference will be formalized in the next section.

In the sequel of the presentation, we limit ourselves to a description of one-dimensional approximation problems. Although the growth in computer power allows for the study of more and more complex models and simulations, the theory of several more-dimensional approximation problems is still not sufficiently complete. We will indicate where up-to-date literature on the more-dimensional generalizations can be found.

Keywords:

  • interpolation;
  • least-squares problems;
  • polynomials;
  • rational functions