非线性最小二乘问题数值迭代法的统一模型及其不适定性

Unified model and ill-posed property of numerical iterative formula for solving nonlinear least squares problem

通过综合归纳在路面模量反算和测量平差等领域中求解非线性最小二乘问题的各种数值迭代解法,建立了非线性最小二乘问题数值迭代法的统一模型.根据不适定问题理论,结合非线性最小二乘问题,定义了非线性最小二乘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,并给出了实例.结果表明,在NLS问题上使用各种数值迭代解法时,需考虑其迭代过程的不适定问题.

All kinds of numerical iterative methods for solving nonlinear least squares problems that widely exists in inverse calculation of pavement modulus and surveying adjustment fields were summarized, a unified model of numerical iterative formula for solving nonlinear least squares problems was proposed. According to ill-posed problem theory, combined with nonlinear least squares problems, two ill-posed properties of nonlinear least squares problems were defined. The phenomenon of the two ill-posed properties was analysis, and some examples were given. The results show that it needs to consider the ill-posed problem in iterative process when all kinds of numerical iterative methods for NLS problems are used.