| 含参变量的三阶方向牛顿法及其收敛性 |
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| 引用本文： | 寇继生,顾颖.含参变量的三阶方向牛顿法及其收敛性[J].应用数学与计算数学学报,2014(2):228-236. |
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| 作者姓名： | 寇继生 顾颖 |
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| 作者单位： | 上海大学理学院,上海200444 |
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| 基金项目： | 上海市教育委员会重点学科建设资助项目（J50101） |
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| 摘 要： | 通过递推关系归纳迭代公式的讨论,研究含多个未知数的非光滑方程组及其收敛性,并以此证明希尔伯特空间上的含参变量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,给出解的存在性以及先验误差界.
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| 关 键 词： | 非线性方程 参程量 方向牛顿法 |
Parametric variable three-order direction Newton method and its convergence |
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| KOU Ji-sheng,GU Ying.Parametric variable three-order direction Newton method and its convergence[J].Communication on Applied Mathematics and Computation,2014(2):228-236. |
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| Authors: | KOU Ji-sheng GU Ying |
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| Institution: | (College of Sciences, Shanghai University, Shanghai 200444, China) |
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| Abstract: | The iterative formula is induced by recursive relations to focus on solving a nonsmooth equation in several unknowns and its convergence. The thirdorder directional Newton method is used to solve nonlinear real operator equations on the Hilbert spaces. The recurrence relations for the method are derived, and then the semilocal convergence of this method is established by using recurrence relations. The prior error bounds is also given. |
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| Keywords: | nonlinear equation parametric variable directional Newton method |
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