| 一阶导数条件下带参数的修正型Euler-Halley迭代族的收敛性 |
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| 引用本文： | 叶新涛,李冲. 一阶导数条件下带参数的修正型Euler-Halley迭代族的收敛性[J]. 数学学报, 2005, 48(5): 901-908. DOI: cnki:ISSN:0583-1431.0.2005-05-009 |
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| 作者姓名： | 叶新涛 李冲 |
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| 作者单位： | [1]南京晓庄学院数学系,南京210038 [2]浙江大学数学系,杭州310027 |
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| 基金项目： | 国家自然科学基金资助项目（10271025） |
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| 摘 要： | 本文研究了Banach空间中非线性算子方程的带参数的修正型Euler-Halley迭代族的收敛性问题.在算子的一阶导数满足Lipschitz条件下建立了修正型Euler-Halley迭代族的半局部二阶收敛性.
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| 关 键 词： | 非线性算子方程 修正型Euler-Halley迭代族 二阶收敛性 |
| 文章编号： | 0583-1431（2005）05-0901-08 |
| 收稿时间： | 2004-03-16 |
| 修稿时间： | 2004-03-162004-07-28 |
Convergence of the Family of Deformed Euler-Halley Iterations with Parmeters under the First Derivative Condition |
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| Xie XinTao;Li Chong. Convergence of the Family of Deformed Euler-Halley Iterations with Parmeters under the First Derivative Condition[J]. Acta Mathematica Sinica, 2005, 48(5): 901-908. DOI: cnki:ISSN:0583-1431.0.2005-05-009 |
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| Authors: | Xie XinTao Li Chong |
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| Affiliation: | Xin Tao YE Department of Mathematics, Nanjing Xiaozhuang Institute, Nanjing 210038, P. R. China Chong LI Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China |
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| Abstract: | The convergence problem of family of the deformed Euler-Halley iterations with parmeters for solving nonlinear operator equations in Banach spaces is studied. Under the assumption that the derivative of the operator satisfies the Lipschitz condition, the semi-local quadratic convergences of the family of deformed Euler-Halley iterations are established. |
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| Keywords: | Nonlinear operator equation The family of the deformed Euler-Halley iterations The quadratic convergence |
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