拟非扩张映像族的平行混杂算法及其数值实验
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摘要
在Hilbert空间中设计出一种新的关于有限族拟非扩张映像的公共不动点的平行混杂算法,并利用投影算子的性质等证明了该算法所生成的序列强收敛于拟非扩张映像族的公共不动点,且给出数值实验说明所提出算法的有效性。
In Hilbert spaces,a new parallel hybrid algorithm for common fixed points of a finite family of quasi-nonexpansive mappings is proposed. A strong convergence theorem for the common fixed points of a finite family of quasi-nonexpansive mappings is proved by using projection operators and other analysis techniques. Some numerical experiments are also included to explain the effectiveness of the proposed algorithm.
In Hilbert spaces,a new parallel hybrid algorithm for common fixed points of a finite family of quasi-nonexpansive mappings is proposed. A strong convergence theorem for the common fixed points of a finite family of quasi-nonexpansive mappings is proved by using projection operators and other analysis techniques. Some numerical experiments are also included to explain the effectiveness of the proposed algorithm.
引文
[1]Yao Y. A general iterative method for a finite family of nonexpansive mappings[J]. Nonlinear Anal,2007,66:2676-2687.
[2]Xu H K. A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem[J]. Inverse Probl,2006,22:2021-2034.
[3]Combettes P L. On the numerical robustness of the parallel projection method in signal synthesis[J]. IEEE Signal Process. Lett,2001,8:45-47.
[4]Podilchuk C I,Mammone R J. Image recovery by convex projections using a least-squares constraint[J]. J. Opt.Soc. Am,1990,7:517-521.
[5]Nakajo K,Takahashi W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups[J].J. Math. Anal. Appl,2003,279:372-379.
[6]Marino G,Xu H K. Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces[J]. J.Math. Anal. Appl,2007,329:336-346.
[7]Gao X H,Ma L R. A new hybrid algorithm and its numerical realizations for a quasi-nonexpansive mapp-ings[J].Communications in Mathematical Research,2017,33(4):340-346.
[8]高兴慧,张朵,李婉亭,等.关于拟渐近伪压缩映像族的混杂算法及其数值实现[J].贵州师范大学学报(自然科学版),2018,35(2):55-58.
[9]高兴慧,魏姣姣,乔田田,等.关于拟渐近伪压缩映像族的复合迭代算法[J].西北大学学报(自然科学版),2017,47(2):162-166.
[10]高兴慧,高怀丽,常乐.平衡问题不动点问题和零点问题的公共元的强收敛定理[J].宁夏大学学报(自然科学版),2016,37(2):135-140.
[11]Anh P K,Chung C V. Parallel hybrid methods for a finite family of relatively nonexpansive mappings[J]. Numer.Func. Anal. Optim,2014,35:649-664.
[2]Xu H K. A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem[J]. Inverse Probl,2006,22:2021-2034.
[3]Combettes P L. On the numerical robustness of the parallel projection method in signal synthesis[J]. IEEE Signal Process. Lett,2001,8:45-47.
[4]Podilchuk C I,Mammone R J. Image recovery by convex projections using a least-squares constraint[J]. J. Opt.Soc. Am,1990,7:517-521.
[5]Nakajo K,Takahashi W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups[J].J. Math. Anal. Appl,2003,279:372-379.
[6]Marino G,Xu H K. Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces[J]. J.Math. Anal. Appl,2007,329:336-346.
[7]Gao X H,Ma L R. A new hybrid algorithm and its numerical realizations for a quasi-nonexpansive mapp-ings[J].Communications in Mathematical Research,2017,33(4):340-346.
[8]高兴慧,张朵,李婉亭,等.关于拟渐近伪压缩映像族的混杂算法及其数值实现[J].贵州师范大学学报(自然科学版),2018,35(2):55-58.
[9]高兴慧,魏姣姣,乔田田,等.关于拟渐近伪压缩映像族的复合迭代算法[J].西北大学学报(自然科学版),2017,47(2):162-166.
[10]高兴慧,高怀丽,常乐.平衡问题不动点问题和零点问题的公共元的强收敛定理[J].宁夏大学学报(自然科学版),2016,37(2):135-140.
[11]Anh P K,Chung C V. Parallel hybrid methods for a finite family of relatively nonexpansive mappings[J]. Numer.Func. Anal. Optim,2014,35:649-664.