A New Method For Solving Nonlinear Least Squares Problem

With the broad application of nonlinear least squares problems, more attentions are paid to the study of the algorithm, and many new methods are advanced in recent years. In this paper methods for nonlinear least squares problems are classified as: methods based on quasi-Newton equation, hybrid methods and self-scaling method. The classification makes the algorithm design much more lucid, and cast light on the algorithm proposed in this paper.Quasi-Newton methods are efficient ones for nonlinear optimization. Combining quasi-Newton methods with the special structure of nonlinear least squares problems is the best way to designing algorithm. In this paper a new quasi-Newton equation proposed by Pan Pingqi is applied to the problems. Combining the new equation with a "product structure" proposed by Huschens, we show a new quasi-Newtonequation A_k+1S_k = , and a new algorithm is established.Zero residual and non-zero residual problems are discussed in different parts in this paper and the algorithm is proven quadratic convergence for zero residual problems and superlinear convergence for non-zero residual problems. Numerical experiments show that the algorithm is feasible.