Chebyshev approximation of the null function by an affine combination of complex exponential functions

Paul Armand (paul.armandunilim.fr)
Joel Benoist (joel.benoistunilim.fr)
Elsa Bousquet (elsa.bousquetetu.unilim.fr)

Abstract: We describe the theoretical solution of an approximation problem that uses a finite weighted sum of complex exponential functions. The problem arises in an optimization model for the design of a telescopes array occurring within optical interferometry for direct imaging in astronomy. The problem is to find the optimal weights and the optimal positions of a regularized spaced array of aligned telescopes, so that the resulting interference function approximates the zero function on a given interval. The solution is given by means of Chebyshev polynomials.

Keywords: Chebyshev approximation, Chebyshev polynomials, complex exponential functions, interferometry, optimization

Category 1: Applications -- Science and Engineering

Citation: XLIM research report - Universite de Limoges (FRANCE)

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Entry Submitted: 09/22/2009
Entry Accepted: 09/22/2009
Entry Last Modified: 05/21/2010

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