For Solving Nonlinear Least Squares Problem, A New Class Of Decomposition Of The Quasi-newton Method

With the comprehensive application of nonlinear least squares problems, more and more attentions have been paid to the study of the algorithms, and many new methods are advanced in recent years. The first part of this paper goes to a thorough review of studies on the methods for nonlinear least squares problems, which can be classified into six major types: Gauss-New methods,methods based on quasi-Newton equation,factorized quasi-Newton methods,hyrid methods and self-scaling methods. The second part of this paper mainly focuses on a new family of scaled factorized Broyden-Like methods for nonlinear least squares problems.This new family is based on Stable factorized quasi-Newton methods and a scaled approximation of the second order term introducing a multiplier. It is shown that the resulting algorithm yields a quadratic convergence for the zero-residual case and a superlinear convergence for nonzero-residual case. In order to compare the new algorithm with some related methods, numerical experiments are also reported.