A Regularization Homotopy Iterative Method for Ill-Posed Nonlinear Least Squares Problem and its Application
A regularization homotopy iterative method established for ill-posed nonlinear least squares problem. Two new regularization parameter selecting strategies are proposed, which are called direct search method and interval division method. The calculation results of nonlinear least squares problems show that the regularization homotopy iterative method and parameter selecting strategies proposed in this paper are correctly and applicable. And also calculation results of nonlinear adjustment of free networks with rank deficiency of Jianglong bridge pier displacement defor-mation monitoring control network show that the method not only decrease the iterative matrix con-dition number, but also make the condition number small fluctuation in full iterative process.
L. M. Tang "A Regularization Homotopy Iterative Method for Ill-Posed Nonlinear Least Squares Problem and its Application", Applied Mechanics and Materials, Vols. 90-93, pp. 3268-3273, 2011