A variation of the Levenberg Marquardt method : an attempt to improve efficiency

Abstract

The Levenberg-Marquardt method is an efficient and popular damped least square technique. This method is a combination between the Gauss and the steepest gradient descent methods, where the amount of damping used in each iteration is central in establishing the behavior of the system. Further, the damping is determined by four parameters, whose optimum values vary from model to model. An inappropriate selection of the damping parameters could trigger a decrease in the rapidness of convergence, a convergence to a local minimum, or system instability. Therefore, finding proper values for these parameters is fundamental in the use of this method and implies a great deal of extra time. This lack of efficiency is considered a disadvantage in comparison to other techniques. In an attempt to eliminate the use of arbitrary damping parameters as well as to improve the rapidness of the method, this work offers a new formulation for damping. Preliminary results show a positive behavior of the new method, which makes self-consistent automatic choices for the damping coefficients. An apparent improvement in efficiency is observed, despite the fact that a matrix determinant is included in the calculation of damping and more computational resources are involved. The savings in time due to the mechanization of the damping calculation seem to compensate for the extra resources. More study will be needed in order to validate or disqualify the proposed method.