Structural and Multidisciplinary Optimization

, Volume 35, Issue 4, pp 327–339

Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions

Open AccessResearch Paper

DOI: 10.1007/s00158-007-0135-1

Cite this article as:
Siem, A.Y.D., de Klerk, E. & den Hertog, D. Struct Multidisc Optim (2008) 35: 327. doi:10.1007/s00158-007-0135-1


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.


(Trigonometric) polynomialsRational functionsSemidefinite programmingRegression(Chebyshev) approximation
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Department of Econometrics and Operations Research/Center for Economic Research (CentER)Tilburg UniversityTilburgThe Netherlands