求解非线性算子方程的梯形牛顿法  

Trapezium Newton′s Method for Nonlinear Operator Equations

作　　者：薛雅萍[1] 吴开谡[1] 刘晓晶[1] 

机构地区：[1]北京化工大学数学系,北京100029

出　　处：《应用泛函分析学报》2009年第1期90-96,共7页Acta Analysis Functionalis Applicata

基　　金：北京化工大学青年科学基金(QN0622)

摘　　要：在Banach空间中研究非线性算子方程F(x)=0的近似求解问题.首先,把实函数数值积分的梯形公式推广到非线性泛函的Bochner积分中来,得到Bochner积分的梯形公式;然后,利用这一公式来构造牛顿迭代法的变形格式,从而得到梯形牛顿法,并在弱条件的α-判据下借助于优函数技巧证明了它的收敛性.The main object of this paper is to investigate the solution of nonlinear operator equation F （x）= 0 in Banach space. First, we generalize the trapezium formula about numerical integral of real function to the Bochner integral of nonlinear functional so that we obtain the trapezium formula of Bochner integral. Then we use the formula to construct modified scheme of Newtonrs iterative method so as to obtain trapezium Newton＇s method. criterion of weak conditions by means of majorizing Futhermore ,we proved its convergence under function.

关 键 词：梯形牛顿法 α-判据 优函数 

分 类 号：O241.7[理学—计算数学]