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一族二阶导数计值迭代方法的收敛性 被引量：1

Convergence for a family of iterations with cubic order which can avoid the computation of the second Frechet-derivative.
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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-Kantorovich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. 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.
作者 刘静 韩丹夫
机构地区 浙江大学数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2006年第1期28-31,共4页 Journal of Zhejiang University（Science Edition）
关键词 BANACH空间 非线性方程 迭代族 递推关系 收敛性 Banach spaces nonlinear equations family of iterations recurrence relations convergence
分类号 O241 [理学—计算数学]
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参考文献6

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二级参考文献3

共引文献8

同被引文献11

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  • 10WANG XinghuaDepartment of Mathematics, Hangzhou University, Hangzhou 310028, China.Convergence on the iteration of Halley family in weak conditions[J].Chinese Science Bulletin,1997,42(7):552-555. 被引量：19

引证文献1

浙江大学学报（理学版）
2006年 第1期

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