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

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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

Fingerprint

Trigonometric Polynomial
Circular function
Polynomial function
Rational function
Non-negative
Real Algebraic Geometry
Norm
Polynomial
Discrete Approximation
Approximation of Functions
Nonnegativity
Semidefinite Programming
Approximation
Simulation Model
Unknown
Methodology

Keywords

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

Cite this

Siem, A. Y. D., de Klerk, E., & den Hertog, D. (2005). Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions. (CentER Discussion Paper; Vol. 2005-73). Tilburg: Operations research.
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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.",
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Siem, AYD, de Klerk, E & den Hertog, D 2005 'Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions' CentER Discussion Paper, vol. 2005-73, Operations research, Tilburg.

Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions. / Siem, A.Y.D.; de Klerk, E.; den Hertog, D.

Tilburg : Operations research, 2005. (CentER Discussion Paper; Vol. 2005-73).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

AU - Siem, A.Y.D.

AU - de Klerk, E.

AU - den Hertog, D.

N1 - Subsequently published in Structural and Multidisciplinary Optimization, 2008 Pagination: 21

PY - 2005

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N2 - 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.

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KW - (trigonometric) polynomials

KW - rational functions

KW - semidefinite programming

KW - regression

KW - (Chebyshev) approximation

M3 - Discussion paper

VL - 2005-73

T3 - CentER Discussion Paper

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

PB - Operations research

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