| 三阶方向牛顿法的收敛性 |
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| 引用本文： | 戴怡文,寇继生.三阶方向牛顿法的收敛性[J].应用数学与计算数学学报,2010,24(2):55-66. |
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| 作者姓名： | 戴怡文 寇继生 |
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| 作者单位： | [1]上海医药高等专科学校,基础部数理组,上海201318 [2]上海大学数学系,上海200444 |
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| 基金项目： | 国家自然科学基金，上海市高校优秀青年教师科研专项基金 |
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| 摘 要： | 通过递推关系,证明了解希尔伯特空间上的实系数非线性方程组的三阶方向牛顿法的半局部收敛性,给出了解的存在性以及先验误差界,最后计算出一些数值结果来证明我们的结论.
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| 关 键 词： | 非线性方程 方向牛顿法 希尔伯特空间 迭代法 |
Convergence of Third-order Directional Newton Method |
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| Dai Yiwen,Kou Jisheng.Convergence of Third-order Directional Newton Method[J].Communication on Applied Mathematics and Computation,2010,24(2):55-66. |
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| Authors: | Dai Yiwen Kou Jisheng |
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| Institution: | Dai Yiwen Kou Jisheng Group of Mathematics and Physics,Department of Basic Courses,Shanghai Institute of Health Sciences,Shanghai 201318,China Department of Mathematics,Shanghai University,Shanghai 200444, China |
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| Abstract: | Third-order directional Newton method is used to solve nonlinear real operator equations on Hilbert spaces.The recurrence relations for the method are derived and then the semilocal convergence of this method is established by using recurrence relations.A priori error bounds is also given.Some numerical results are presented to demonstrate our approach. |
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| Keywords: | nonlinear equations directional Newton method Hilbert space iterative method |
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