An Alternating Iterative Method For Solving Separable Nonlinear Least Squares Problems

The separable nonlinear least squares(SNLLS)problems can be regarded as a special form of least squares problems.The fitting function of SNLLS problems is a linear combination of nonlinear functions,the parameters to be solved can be divided into two groups,one is the linear combination coefficients,and the other is nonlinear parameters in nonlinear functions.The SNLLS problems are popular in system identification,machine learning,neural networks,etc.Therefore,it has important theoretical and practical significance to study SNLLS problems.The variable projection(VP)method is a common approach to solve SNLLS problems.In this paper,an effective regularization method is proposed to solve the linear equations which are appearing in the VP method.And select the regularization parameter by generalized cross-validation method at every iteration,then design the alternating iteration method to solve the regularization model.The numerical results demonstrate that the algorithm is effective.