非线性最小二乘法的算法

本给出非线性最小二乘的优化条件和几何特征．

Some algorithms of nonlinear least squares

First this paper gives the optimal condition and its geometrical characters of nonlinear least squares.Then gradient and orthogonal gradient algorithms for solving nonlinear parametric model are presented,which expand the Newton-Raphson and Gauss-Newton iteration methods.Finally,the relation between the expectation surface and least squares is addressed.Based on the above,high-ranking approximative method is put forward,which expands the method of linear approximation and has higher accuracy.