Choosing different primary models to invert a set of test resistivity sounding curves derived from a known model, according to the demands on primary models and convergent velocity, this paper compares singular value decomposition method with damping least square method.

This paper presents an optimum estimation algorithm, damped least square method,combining the merit of Newton combines with the that of the rapidest descend for nonlinear time series ARMA parameter estimation.

On the basis of analyzing the whole bag of tricks of spherical surface test, I have researched the damped least square method and established the mathematic and physical model of calculating radius of spherical surface by using the damped least square method.

The damped least square method was applied in both identification of the linear model and study of the neural network.

A convergence analysis of a more stable identification algorithm_recursive damped least square is proposed.

The theory and digitization experiment indicate that the damped least squares method is better in processing the bigger errors.

When optimizing optical systems with the damped least squares method, the solution obtained is usually a local minimum of the merit function in the multi dimensional space of the construction variables.

As refinde algorithms based on Davidon least squares algorithm and damped least squares,not only do they enjoy the advantages of the two algorithms,simple and convenient to be used,having a fast convergent rate,etc,but they can improve the identification accuracy desired and have less computation.

In this approach the network structure is determined by multiresolution learning, and the weights are trained by damped least squares which has fast convergent rate.

This type of global optimization consists of many local optimization runs with or without the excape function using the damped least squares method.