ALGORITHM BASED ON LANDWEBER ITERATION FOR SOLVING RANK DEFICIENCY NONLINEAR LEAST SQUARES PROBLEM
基于Landweber迭代的秩亏非线性最小二乘问题算法研究

More methods such as the gauss-newton method or modified gauss-newton method will failure when the iteration matrix is rank-deficient or very ill-conditioned in solving ill-posed nonlinear least squares problem. Nonlinear Landweber iteration formula x_(k+1)~δ=x_k~δ-f'(x_k~δ)~*(f(x_k~δ)-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 1/ω instead of (B'(x_k)B(x_k)), a new Landweber iteration formula x_(k+1)~δ=x_k~δ-ω(B'(x_k~δ)B(x_k~δ))~*B'(x_k~δ)(f(x_k~δ)-y~δ) is constructed for solving rank deficiency nonlinear least squares problem, with which the phenomenon that leads to ill-posed problem because the iteration matrix is rank-deficient and very ill-conditioned 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.