Discrete Least-Norm Approximation by Nonnegative (Trigonometric) Polynomials and Rational Functions
CentER Discussion Paper No. 2005-73
20 Pages Posted: 11 Jul 2005
Date Written: June 2005
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: Suggested Citation