Covariances of Smoothed Observational Data

Abstract

The method of smoothing observational data in its original form [2–3] did not allow the uncertainties of either the individual smoothed values or their function to be estimated. The present paper, using the same original system of linear equations but a different method for solving them (Cholesky decomposition instead of Gauss elimination), describes an algorithm to compute the covariances of the smoothed data in any selected band. These enable the uncertainties of any function of the smoothed values to be calculated.