2步非线性共轭梯度(NCG)法  

A 2 step Nonlinear Conjugate Gradient (NCG) Method

作　　者：邓玲[1] 李庆扬[1] 

机构地区：[1]清华大学应用数学系

出　　处：《工程数学学报》1998年第2期1-9,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金

摘　　要：提出一种求解非线性方程组的２步非线性共轭梯度法（２步ＮＣＧ法），并在一定条件下证明方法收敛于一个总体唯一解。这个方法收敛较快且适合于并行计算，数值试验表明它比普通ＮＣＧ法迭代次数减少较多，从而节省ＣＰＵ时间。Abstract In this paper, a 2 step nonlinear conjugate gradient method (2 step NCG method) for solving nonlinear equations has been presented, and is proved to converge to a globally unique solution under some conditions. This method is faster than plain NCG method and fits for parallel computing. Numerical experimets show that 2 step NCG method decreases iterative step number many, also decreases CPU time.

关 键 词：非线性方程组 2步非线性共轭梯度法 2步NCG法 唯一解 收敛性 计算公式 预处理算法 数值试验 

分 类 号：O241.7[理学—计算数学]