对最小二乘问题的研究

A New Method of Solving Problem for Nonlinear Least Square

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解法来实现的。他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 ,他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 。

A new method of solving the problem of nonlinear least square is given.This method is constructive by use of the method to solve the system of nonlinear equations.That is,based on solving the 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 method.