Accelerated Levenbert-Marquardt algorithm for nonlinear least squares problems

Abstract

This paper presents modifications of the Levenberg-Marquardt method for solving nonlinear least squares problems. This is of practical importance in various fields such as curve-fitting and parameter estimation. The modifications are made in such a way that, (1) Ruhe's conjugate gradient acceleration is used along with the Levenberg-Marquardt search direction; (2) A modified version of Al-Baali and Fletcher's line search scheme is incorporated into the algorithm in which polynomial interpolations are made to the individual residual functions rather than the overall objective function; (3) Accuracy of the line search is controlled dynamically by letting the accuracy parameters be varied as the norms of the function and gradient change. The algorithm has been implemented using FORTRAN 77, and compared with some other nonlinear least squares codes. Numerical results on a set of test problems indicate that it is efficient as well as robust.