| 一族二阶导数计值迭代方法的收敛性 |
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| 引用本文： | 刘静,韩丹夫. 一族二阶导数计值迭代方法的收敛性[J]. 浙江大学学报(理学版), 2006, 33(1): 28-31 |
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| 作者姓名： | 刘静 韩丹夫 |
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| 作者单位： | 1. 浙江大学,数学系,浙江,杭州,310028;浙江财经学院,数学与统计学院,浙江,杭州,310012
2. 浙江大学,数学系,浙江,杭州,310028 |
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| 摘 要： | 从带一个参数的三阶迭代族(其中包括Halley迭代,Chebyshev迭代和超Halley迭代)出发,推出避免二阶导数计算的带两个参数的迭代族.在Newton-antorovich型的假设条件下,通过用一个递推关系证明了此迭代族的三阶收敛性,并给出了非线性算子方程解的存在惟一性定理.
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| 关 键 词： | Banach空间 非线性方程 迭代族 递推关系 收敛性 |
| 文章编号： | 1008-9497(2006)01-028-04 |
| 收稿时间： | 2004-04-30 |
| 修稿时间： | 2004-04-30 |
Convergence for a family of iterations with cubic order which can avoid the computation of the second Frechet-derivative |
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| LIU Jing,HAN Dan-fu. Convergence for a family of iterations with cubic order which can avoid the computation of the second Frechet-derivative[J]. Journal of Zhejiang University(Sciences Edition), 2006, 33(1): 28-31 |
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| Authors: | LIU Jing HAN Dan-fu |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310028, China; 2. Zhejiang University of Finance and Economics, Hangzhou 310012, China |
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| Abstract: | A family of iterations with two parameters which can avoid the computation of the second Frechet-derivatire is introduced. Using Newton-Katorovih type assumption, a convergent theorem for the family of iterations is established, and the result on the existence of a unique solution to the nonlinear equation is given by using a technique based on a new system of recurrence relations. |
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| Keywords: | Banach spaces nonlinear equations family of iterations recurrence relations convergence |
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