An algorithm for least squares analysis of spectroscopic data

Abstract

Abstract.This paper describes a variant of the Gauss-Newton-Hartley algorithm for nonlinear least squares, in which a QR implementation is used to solve the linear least squares problem. We follow Grey's idea of updating variables at intermediate stages of the orthogonalization. This technique, applied in partitions identified with known or suspected spectral lines, appears to be especially suited to the analysis of spectroscopic data. We suggest that this algorithm is an attractive candidate for the optimization role in Ekenberg's interactive computer graphics curve fitting program.