| 避免二阶导数计值的迭代族在一阶Frechet可微条件下的收敛性 |
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| 引用本文： | 刘静.避免二阶导数计值的迭代族在一阶Frechet可微条件下的收敛性[J].浙江大学学报(理学版),2005,32(6):627-630. |
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| 作者姓名： | 刘静 |
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| 作者单位： | 浙江财经学院,数学与统计学院,浙江,杭州,310012;浙江大学,数学系,浙江,杭州,310028 |
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| 摘 要： | 介绍一族避免二阶导数计值的带两个参数的迭代法来近似Banach空间中非线性方程的解.在与Newton法收敛相同的Lipschitz条件下,通过用一个递推关系证明了此迭代族的收敛,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 迭代族 递推关系 收敛性 |
| 文章编号： | 1008-9497(2005)06-627-04 |
| 收稿时间： | 2004-03-23 |
| 修稿时间： | 2004年3月23日 |
Convergence for a family of iterations which an avoid the computation of the second Frechet-derirative under the Lipschitz condition |
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| LIU Jing.Convergence for a family of iterations which an avoid the computation of the second Frechet-derirative under the Lipschitz condition[J].Journal of Zhejiang University(Sciences Edition),2005,32(6):627-630. |
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| Authors: | LIU Jing |
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| Institution: | 1. Zhejiang University of Finance and Economics, Hangzhou 310012, China; 2. Department of Mathematics, Zhejiang University, Hangzhou 310028, China |
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| Abstract: | A new family of the second-order-derivative-free iterations with two parameters is introduced to approximate a solution of a nonlinear equation in Banach spaces.Under the same Lipschitz conditon as for Newton's method,a convergent theorem for the family of iterations is established,and the result on the existence of a unique solution for the nonlinear equation by using a technique based on a new system of recurrence relations is given. |
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| Keywords: | Banach spaces a family of iterations recurrence relations convergence |
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