全局收敛的非线性最小二乘在Forstat中的实现

Implementation of nonlinear least square with global convergence in Forstat

非线性最小二乘问题大多具有实际背景,在林业、生态等领域的模型建立中有着重要的作用。针对其算法通常存在的局部收敛问题,采用信赖域法,并综合考虑迭代过程中溢出问题和用于模型判断的残差图绘制,在Forstat中设计和实现了全局收敛的非线性最小二乘。数值实验表明:算法有极好的精确性和较好的全局收敛性与稳定性。建立非线性模型时,在待求参数没有先验知识的情况下,可以得到较好的结果。

Most problems of nonlinear least square have practical background,and play important parts in the model establishing of such fields as forestry,ecology.Using trust region method to solve local convergence of the usual arithmetic,correcting the over-flow in the process of iterative and protracting the chart of residual sum of square to diagnose model.Nonlinear least square with the global convergence has been designed and implemented in the Forstat.The numeric test shows the algorithm is accurate,stable and globally convergent.It is useful for nonlinear modal without any previous known parameters.