摘要
给出了一种求解非线性对称方程组的无导数下降法.该算法可以看成为最速下降法和共轭梯度法的扩展.由于储存量小,这种算法对于大型非线性方程也有效.当F的雅可比矩阵F′(x)关于有界集Ω={x∈Rn|θ(x)≤θ(x0)}中的x对称时,证明了算法具有全局收敛性.
A derivative-free method for solving nonlinear equations is put forward. The method can be regarded as extensions of the steepest descent method and the conjugate gradient method. Due to lower storage,it can be applied to solve large scale nonlinear equations. That the method is globally convergent is proven,when the Jacobian F＇（ x）of F is symmetric for every x ∈Ω= { x ∈ R^n｜ θ （ x ） ≤θ （ x0）}.
出处
《湖南文理学院学报（自然科学版）》
CAS
2010年第2期24-25,28,共3页
Journal of Hunan University of Arts and Science(Science and Technology)
关键词
非线性对称方程组
无导数法
下降方向
全局收敛性
nonlinear symmetric equations
derivative-free methods
descent direction
global convergence
