[1]罗俊[],刘健[]. Hilbert 空间上多集合分裂可行问题的KM 迭代算法[J].计算机技术与发展,2016,26(01):43-47.
　LUO Jun[],LIU Jian[]. KM Iterative Algorithm for Multiple-sets Split Feasibility Problem in Hilbert Space[J].,2016,26(01):43-47.
点击复制

 Hilbert 空间上多集合分裂可行问题的KM 迭代算法()
分享到：

《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
26
期数:
2016年01期
页码:
43-47
栏目:
智能、算法、系统工程
出版日期:
2016-01-10

文章信息/Info

Title:
 KM Iterative Algorithm for Multiple-sets Split Feasibility Problem in Hilbert Space
文章编号:
1673-629X（2016)01-0043-05
作者:
 罗俊[1]; 刘健[2]
 1.南京邮电大学 理学院；2.南京邮电大学 通信与信息工程学院
Author(s):
 LUO Jun[1]; LIU Jian[2]
关键词:
 ; 多集合分裂可行问题; 优化问题; KM 迭代; Hilbert 空间
Keywords:
 ; multiple-sets split-feasibility problem; optimization problem; KM iteration; Hilbert Space
分类号:
TP301.6
文献标志码:
A
摘要:
 多集合分裂可行问题就是寻找与一族非空闭凸集距离最近的点，并使得该点在线性变换下的像与另一族非空闭凸集的距离最近。分裂可行问题是一类重要的最优化问题，产生于工程实践，在医学、信号处理和图像重建等领域中有着广泛的应用。文中基于 n 维线性空间上求解分裂可行问题的 KM 迭代算法，目的是要将算法在 Hilbert 空间中加以推广应用。通过在 Hilbert 空间中运用投影压缩定理，并且利用逼近函数将多集合分裂可行问题转化为最小值问题，方便了对算法的推导证明。利用上述方法可得，多集合分裂可行问题的 KM 迭代算法在 Hilbert 空间中也有较好的收敛性。因此，可以将多集合分裂可行问题的 KM 迭代算法在 Hilbert 空间中加以推广。
Abstract:
 he multiple-sets spilt feasibility problem requires finding a point closest to a family of closed convex sets in one space,so that its image under a linear transformation will be closest to another family of closed convex sets in the image space. The multiple-sets spilt feasibility problem is an important type of optimization problem,which is generated from engineering practice and already has been wide-ly applied in medical science,signal processing,image reconstruction. Based on KM iterative methods for solving the multiple-sets spilt feasibility problem in Rn space,try to spread this algorithm in Hilbert Space. Using projection compression theorem and approximation function transformed the multiple-sets spilt feasibility problem into a minimum value problem,making the algorithm proving more easily. By deducing and proving,the multiple-sets spilt feasibility problem has good convergence in Hilbert Space. So the result shows that the KM iterative methods are spread in Hilbert Space perfectly.

相似文献/References:

[1]张志宏,吴庆波,邵立松,等.基于飞腾平台TOE协议栈的设计与实现[J].计算机技术与发展,2014,24(07):1.
　ZHANG Zhi-hong,WU Qing-bo,SHAO Li-song,et al. Design and Implementation of TCP/IP Offload Engine Protocol Stack Based on FT Platform[J].,2014,24(01):1.
[2]梁文快,李毅. 改进的基因表达算法对航班优化排序问题研究[J].计算机技术与发展,2014,24(07):5.
　LIANG Wen-kuai,LI Yi. Research on Optimization of Flight Scheduling Problem Based on Improved Gene Expression Algorithm[J].,2014,24(01):5.
[3]黄静,王枫,谢志新,等. EAST文档管理系统的设计与实现[J].计算机技术与发展,2014,24(07):13.
　HUANG Jing,WANG Feng,XIE Zhi-xin,et al. Design and Implementation of EAST Document Management System[J].,2014,24(01):13.
[4]侯善江[],张代远[][][]. 基于样条权函数神经网络P2P流量识别方法[J].计算机技术与发展,2014,24(07):21.
　HOU Shan-jiang[],ZHANG Dai-yuan[][][]. P2P Traffic Identification Based on Spline Weight Function Neural Network[J].,2014,24(01):21.
[5]李璨,耿国华,李康,等. 一种基于三维模型的文物碎片线图生成方法[J].计算机技术与发展,2014,24(07):25.
　LI Can,GENG Guo-hua,LI Kang,et al. A Method of Obtaining Cultural Debris’ s Line Chart Based on Three-dimensional Model[J].,2014,24(01):25.
[6]翁鹤,皮德常. 混沌RBF神经网络异常检测算法[J].计算机技术与发展,2014,24(07):29.
　WENG He,PI De-chang. Chaotic RBF Neural Network Anomaly Detection Algorithm[J].,2014,24(01):29.
[7]刘茜[],荆晓远[],李文倩[],等. 基于流形学习的正交稀疏保留投影[J].计算机技术与发展,2014,24(07):34.
　LIU Qian[],JING Xiao-yuan[,LI Wen-qian[],et al. Orthogonal Sparsity Preserving Projections Based on Manifold Learning[J].,2014,24(01):34.
[8]尚福华,李想,巩淼. 基于模糊框架-产生式知识表示及推理研究[J].计算机技术与发展,2014,24(07):38.
　SHANG Fu-hua,LI Xiang,GONG Miao. Research on Knowledge Representation and Inference Based on Fuzzy Framework-production[J].,2014,24(01):38.
[9]叶偲,李良福,肖樟树. 一种去除运动目标重影的图像镶嵌方法研究[J].计算机技术与发展,2014,24(07):43.
　YE Si,LI Liang-fu,XIAO Zhang-shu. Research of an Image Mosaic Method for Removing Ghost of Moving Targets[J].,2014,24(01):43.
[10]余松平[][],蔡志平[],吴建进[],等. GSM-R信令监测选择录音系统设计与实现[J].计算机技术与发展,2014,24(07):47.
　YU Song-ping[][],CAI Zhi-ping[] WU Jian-jin[],GU Feng-zhi[]. Design and Implementation of an Optional Voice Recording System Based on GSM-R Signaling Monitoring[J].,2014,24(01):47.
[11]王前芬,张九玲,罗俊. 求解多集合分裂可行问题的不精确投影算法[J].计算机技术与发展,2015,25(02):9092.
　WANG Qian-fen,ZHANG Jiu-ling,LUO Jun. Inexact Projection Methods for Solving Multiple-sets Split Feasibility Problem[J].,2015,25(01):9092.

更新日期/Last Update: 2016-04-12