NLS问题的不适定性及正则化解算方法

本文进一步完善定义了NLS问题的两种不适定性,对产生这两种不适定问题的现象进行了分析。借助于正则化理论,通过添加稳定泛函,结合高斯-牛顿法,构造了不适定NLS问题的正则化高斯-牛顿法求解公式;解决了普通高斯-牛顿法在迭代过程中其Jacobian矩阵是秩亏或者严重病态导致的不能收敛的问题;给出了非线性秩亏自由网平差的正则化高斯-牛顿法步骤;以几个经典NLS问题为例进行了数值实验,说明了本文所提方法的适用性。

I11 -posed property and regularization solving method for NLS problems

Two ill-posed properties of NLS problems were defined in the paper.The phenomenon of the two ill-posed properties was analyzed.Based on regularization theory,by adding stable function and binding with gauss-newton method,this paper constructed regularization gauss-newton method for solving ill-posed nonlinear least squares problem.The method solved the difficulties that lead to not convergence because the Jacobian matrix is rank-deficient and very ill-conditioned in numerical iterative process.The procedure of this method for solving nonlinear adjustment of free networks with rank deficiency was put forward.Numerical experiment showed that the method which this paper given is accuracy and applicable by testified examples.