一个求解非线性最小二乘问题的新方法  

A New Method of Solving Problem of Nonlinear Least Square

作　　者：陈淑铭[1] 乔田田[2] 

机构地区：[1]烟台大学数学与信息科学系,山东烟台264005 [2]石油大学数学与计算科学学院,山东东营257061

出　　处：《烟台大学学报（自然科学与工程版）》2004年第1期14-22,共9页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：山东省自然科学基金资助项目(Q99A09).

摘　　要：在Gauss Newton(G N)方法和Levenbery Marquardt(L M)方法(阻尼最小二乘法)的基础上给出了一种新的求解非线性最小二乘问题的方法,它是通过寻求新的非线性方程组的数值方法来实现的.首先给出了不用计算导数的求解非线性方程组的收敛迭代方法,该方法是建立在求解动力系统的稳定点的基础上,采用了较稳定的常微分方程初值问题的数值方法进行迭代求解,并采用Steffensen加速技术以提高收敛速度.最后,给出了用Matlab试算的数值例子.试验结果表明了该方法的有效性.Based on Gauss-Newton method and Levenbery-Marquardt method, a new method of solving problem of nonlinear least square is given. This method is constructed by use of the method to solving system of nonlinear equations. That is, based on solving stable point of dynamic system, the convergent iterative method of solving system of nonlinear equations without employing derivatives is established where the stable method of solving initial value problem for ordinary differential equation are used. If the approximation is near to the solution, the technique of Steffensen accelerating is used to improve convergence rate of this iterative methods. At last, some of numerical examples are computed with Matlab. Numerical results show that the method is effective.

关 键 词：非线性最小二乘 Gauss-Newton方法 阻尼最小二乘法 LM方法 李雅普诺夫方法 Steffensen加速 

分 类 号：O241.5[理学—计算数学] O241.7[理学—数学]