Gauss-Newton BFGS方法所产生的迭代矩阵序列的收敛性

The Convergence of Iterate Matrices Sequences Generated by Gauss-Newton BFGS Methods

收敛速度的快慢是决定一个算法好坏的重要因素。在拟牛顿算法中,算法的收敛性在某种程度上等价于Dennis-Moré条件,但这并不意味着算法所产生的迭代矩阵就会收敛到Hessian矩阵。本文证明了由求解对称非线性方程组的Gauss-Newton BFGS方法所产生的迭代矩阵序列的收敛性,并通过数值实验对结论进行验证。

The speed of convergence is an important factor that determines the quality of an algorithm. In the quasi-Newton algorithm, the convergence of the algorithm is equivalent to the Dennis-Morécondi-tion to some extent, but this does not mean that the iterative matrix generated by the algorithm will converge to the Hessian matrix. This paper proves the convergence of the iterative matrix se-quence generated by the Gauss-Newton BFGS method for solving symmetric nonlinear equations, and validates the conclusion by numerical experiments.