弱条件下若干变形牛顿迭代的收敛性  

Convergence on deformed Newton's iteraions under weak conditions.

作　　者：蒋冬冬[1] 沈硕[1] 

机构地区：[1]浙江大学数学系

出　　处：《浙江大学学报（理学版）》2003年第2期136-139,共4页Journal of Zhejiang University（Science Edition）

摘　　要：各种变形牛顿迭代法在解不同复杂程度的非线性方程 f(x) =0时有各自的优缺点 .在 Smale点估计理论引导下 ,作者利用优序列方法 ,研究了弱条件下 ,减少导映照计值次数、避免导映照求逆两种变形牛顿迭代在求解时的收敛性问题 .对此两种迭代法分别建立了各自的收敛性定理 .证明了在弱条件下 ,两种方法产生的迭代序列均收敛于 f(x) =0的惟一零点 。Recently, more and more deformed Newton's iterations have appeared. They each present their advantages and disadvantages in solving different equations. By means of Smale's point estimates and the majorant method, the convergence of two deformed Newton's iterations under weak conditions is studied. The convergence of the iteration's sequences to the solution under weak conditions and error estimates are also given.

关 键 词：弱条件 变形牛顿迭代 收敛性 优序列方法 Γ-条件 非线性方程 Smale点估计理论 牛顿法 

分 类 号：O242.23[理学—计算数学]