ALGORITHM BASED ON LANDWEBER ITERATION FOR SOLVING
RANK DEFICIENCY NONLINEAR LEAST SQUARES PROBLEM
Tang Limin 1,2) ; and Zhu Jianjun 1)
1)School of InfoPhysics and Geomatics Engineering of Central South University, Changsha 4100832)School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410004
Abstract：More methods such as the gaussnewton method or modified gauss-newton method will failure when the iteration matrix is rankdeficient or very illconditioned in solving illposed nonlinear least squares problem. Nonlinear Landweber iteration formula x δ k+1=x δ k-f′(x δ k) *(f(x δ k)-y δ)
is analyzed and a new method is derived. On the basis of the conversion relation of inverse matrix and adjoint matrix, by using [WTBX]1/ω instead of |(B′(x k)B(x k))|，
a new Landweber iteration formula
x δ k+1=x δ k-ω(B′(x δ k)B(x δ k)) *B′(x δ k)(f(x δ k)-y δ)
is constructed for solving rank deficiency nonlinear least squares problem, with which the phenomenon that leads to illposed problem because the iteration matrix is rankdeficient and very illconditioned in numerical iterative process is avoided. The numerical experiment showes that the new Landweber iteration formula is accurate and of applicability for nonlinear adjustment of free networks with rank deficiency and rank deficiency nonlinear least squares problems.
Tang Limin,and Zhu Jianjun . ALGORITHM BASED ON LANDWEBER ITERATION FOR SOLVING
RANK DEFICIENCY NONLINEAR LEAST SQUARES PROBLEM [J]. jgg, 2010, 30(1): 95-98.
