Structural and Multidisciplinary Optimization

, Volume 35, Issue 4, pp 327–339 | Cite as

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

Open Access
Research Paper

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.

Keywords

(Trigonometric) polynomials Rational functions Semidefinite programming Regression (Chebyshev) approximation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

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

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