| Hilbert空间中求解分裂可行问题CQ算法的强收敛性 |
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| 引用本文： | 赵世莲. Hilbert空间中求解分裂可行问题CQ算法的强收敛性[J]. 应用数学和力学, 2019, 40(1): 108-114. DOI: 10.21656/1000-0887.390012 |
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| 作者姓名： | 赵世莲 |
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| 作者单位： | 西华师范大学 数学与信息学院, 四川 南充637002 |
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| 基金项目： | 国家自然科学基金（11371015） |
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| 摘 要： | 在Hilbert空间中,为了研究分裂可行问题迭代算法的强收敛性,提出了一种新的CQ算法.首先利用CQ算法构造了一个改进的Halpern迭代序列;然后通过把分裂可行问题转化为算子不动点,在较弱的条件下,证明了该序列强收敛到分裂可行问题的一个解.推广了Wang和Xu的有关结果.
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| 关 键 词： | 分裂可行问题 强收敛 CQ算法 改进的Halpern迭代 |
| 收稿时间： | 2018-01-08 |
Strong Convergence of CQ Algorithms for Split Feasibility Problems in the Hilbert Spaces |
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| ZHAO Shilian. Strong Convergence of CQ Algorithms for Split Feasibility Problems in the Hilbert Spaces[J]. Applied Mathematics and Mechanics, 2019, 40(1): 108-114. DOI: 10.21656/1000-0887.390012 |
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| Authors: | ZHAO Shilian |
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| Affiliation: | School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, P.R.China |
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| Abstract: | To study the strong convergence of split feasibility problems, a new CQ algorithm was proposed in the Hilbert spaces. Firstly, the modified Halpern iterative sequence was obtained with the CQ method. Furthermore, the split feasibility problem was transformed into the fixed point for operators, and it was proved that the sequence converges strongly to a solution of the split feasibility problem under some weak conditions. The findings generalize the corresponding results of Wang and Xu. |
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| Keywords: | split feasibility problem strong convergence CQ method modified Halpern iteration |
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