### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 21 |

Volume | 2005-73 |

Publication status | Published - 2005 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2005-73 |

### Fingerprint

### Keywords

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

### Cite this

*Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions*. (CentER Discussion Paper; Vol. 2005-73). Tilburg: Operations research.

}

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

Research output: Working paper › Discussion paper › Other 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

Y1 - 2005

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.

AB - 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.

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

CY - Tilburg

ER -