Molecular spectroscopy aims at determining molecular parameters from spectroscopic data. The system of linear equations, the conditional equations, connecting the parameters and the experimental data is frequently nearly singular because some of the parameters are not too well defined by the experiment. Traditionally the least-squares solution to these equations is found from the corresponding normal equations, but if the conditional equations are nearly singular, it is better to solve them by use of a singular value decomposition of the coefficient matrix. The presence of near singularities is clearly signalized and identified, and the least-squares solution is easily computed. This well-known method is outlined, and the introduction of damping factors is proposed. The choice of the damping factors is discussed in some detail. Damping factors are especially useful if the connection between the parameters and the experimental data is nonlinear, so that an iteration is needed to find the best values of the parameters. © 1990.
