EDP Sciences
Free access
Volume 395, Number 2, November IV 2002
Page(s) 733 - 745
Section Computational methods
DOI http://dx.doi.org/10.1051/0004-6361:20021293

A&A 395, 733-745 (2002)
DOI: 10.1051/0004-6361:20021293

Interpolation and smoothing

M. Lombardi

Institut für Astrophysik und Extraterrestrische Forschung, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

(Received 12 April 2002 / Accepted 26 August 2002 )

Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different interpolation techniques are very poorly known. In this paper, we consider the general problem of interpolating discrete data whose location measurements are distributed on the sky according to a known density distribution (with or without clustering). We derive expressions for the expectation value and for the covariance of the smoothed map for many interpolation techniques, and obtain a general method that can be used to obtain these quantities for any linear smoothing. Moreover, we show that few basic properties of smoothing procedures have important consequences on the statistical properties of the smoothed map. Our analysis allows one to obtain the statistical properties of an arbitrary interpolation procedure, and thus to optimally choose the technique that is most suitable for one's needs.

Key words: methods: statistical -- methods: analytical -- methods: data analysis -- gravitational lensing

© ESO 2002