Discrete Least-Norm Approximation by Nonnegative (Trigonometric) Polynomials and Rational Functions

CentER Discussion Paper No. 2005-73

20 Pages Posted: 11 Jul 2005

See all articles by A.Y.D. Siem

A.Y.D. Siem

Tilburg University - Department of Econometrics & Operations Research

Etienne de Klerk

Tilburg University

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: June 2005

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

JEL Classification: C60

Suggested Citation

Siem, A.Y.D. and de Klerk, Etienne and den Hertog, Dick, Discrete Least-Norm Approximation by Nonnegative (Trigonometric) Polynomials and Rational Functions (June 2005). CentER Discussion Paper No. 2005-73. Available at SSRN: https://ssrn.com/abstract=756346 or http://dx.doi.org/10.2139/ssrn.756346

A.Y.D. Siem (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O.Box 90153
5000 LE Tilburg
Netherlands

Etienne De Klerk

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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