REGULARIZATION HOMOTOPY METHOD FORSOLVING ILL-POSED NONLINEAR LEAST SQUARE PROBLEM AND ITS APPLICATION
Tang Limin 1,2) ; and Zhu Jianjun 1)
1)School of Info-Physics and Geomatics Engineering of Central South University, Changsha 4100832)School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410004
Abstract：A regularization homotopy function is constructed for solving the illposed nonlinear least squares problem whose Jacobian matrix is rankdeficient or very illconditioned. A regularization homotopy iterative formula is established for illposed nonlinear least squares problem. The iterative process is derived in detial and the continuity and convergence conditions are given as well. Two new regularization parameter selecting strategies are proposed, which called as direct search method and interval division method. The calculation results of nonlinear least squares problems show that the method is correctly and applicable. Calculation results of nonlinear adjustment of free networks with rank deficiency examples also show that the method not only decrease the iterative matrix condition number, but also make the condition number small fluctuation in the total iterative process, so that a smaller stable norm solution can be obtained.
