Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

A.Y.D. Siem, E. de Klerk, D. den Hertog

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Abstract

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages21
Volume2005-73
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-73

Keywords

  • (trigonometric) polynomials
  • rational functions
  • semidefinite programming
  • regression
  • (Chebyshev) approximation

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