Modern ideas in data reduction

Data resolution is an important task in astronomy, one that is generally undertaken using the method of least squares. But mathematically the least squares criterion is only one of an infinite number of ways to minimize the p-th norm of the vector of residuals. Nevertheless, given certain assumptions one can show that the least squares solution is the best. Various alternative techniques for reducing data are presented. For a badly conditioned system a least squares reduction by orthogonal triangularization (Givens, Householder) may be useful. Iteratively reweighted least squares is a robust least squares procedure. The L₁ method is a robust, non-least squares procedure for solving an overdetermined system. A comparison of a least squares and an L₁ solution, with their respective errors, should give a good idea of the real errors present in the system.Asociación Argentina de Astronomí