| 鞍点问题的HSS-GS迭代法与收敛理论 |
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| 引用本文： | 陈芳,左军.鞍点问题的HSS-GS迭代法与收敛理论[J].北京机械工业学院学报,2014(4):25-29. |
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| 作者姓名： | 陈芳 左军 |
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| 作者单位： | 北京信息科技大学理学院,北京100192 |
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| 基金项目： | 北京市教委面上项目（KM201411232018）;北京信息科技大学学校基金科研项目（1425033） |
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| 摘 要： | 为了更好地求解鞍点问题,提出了埃尔米特和反埃尔米特分裂-类高斯赛德尔(HSS-GS)交替迭代法,并分析了其收敛性质。由于鞍点问题是二阶分块矩阵,且最后一块是零矩阵,通过引入新的矩阵,可以得到求解鞍点问题的类高斯赛德尔(GS-like)方法,并给出了相应的收敛性质。进一步,在GS-like方法和HSS迭代法的基础上,给出了HSS-GS交替迭代方法,并分析了这类算法的收敛性质。数值算例表明,GS-like方法和HSS-GS迭代法都可行,且后者更加有效。
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| 关 键 词： | 鞍点问题 GS-like方法 HSS-GS迭代法 |
HSS-GS iterative method and convergence theory of saddle point problem |
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| CHEN Fang,ZUO Jun.HSS-GS iterative method and convergence theory of saddle point problem[J].Journal of Beijing Institute of Machinery,2014(4):25-29. |
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| Authors: | CHEN Fang ZUO Jun |
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| Affiliation: | (School of Applied Science, Beijing Information Science and Technology University,Beijing 100192 ,China) |
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| Abstract: | The Hermitian skew-Hermitian splitting-Guass-Seidel （HSS-GS） iterative method of saddle point problem is studied, and its convergence property is analyzed. The saddle point problem is second-order block matrix, and the last block is zero matrix. By using the new matrix, the GS-like method and its convergence properties are gained. Based on the GS-like and HSS iterative methods, the HSS-GS iterative method is proposed and the convergence is analyzed. Numerical results show the feasibility of GS- like and HSS-GS iterative methods, and the latter is more effective. |
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| Keywords: | saddle point problems GS-like method HSS-GS iterative method |
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