关于具矩阵三角分解修正拟Newton法的收敛性分析

Convergence Analysis for a Class of Matrix Factorization Update Quasi-Newton Methods

本文对于Johnson、Austria提出的求解非线性方程组的基于矩阵三角分解修正的一类拟Newton法进行了改形,并给出了该算法的Kantorovich型的收敛性分析,从而完整了文(l]的收敛理论,亦为算法的初始选取,提供了依据.

In this paper, we give a variant and its Kantorovich-type analysis for the class of matrix factorization update Quasi-Newton methods of solving nonlinear systems of equation F(x)=0, F:DR^n→R^n which has been posed by Johnson and Austria. Thus the convergence theory in [1] is completed. This work also affords an essential criterion for the initial value selection of the methods. At the last of this paper, we discuss the generalization of the method for large scale sparse nonlinear systems of equation.