| 求解具有多个右端项线性方程组的总体GMERR算法 |
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| 引用本文： | 郑玉晖,程东旭,钱晓惠.求解具有多个右端项线性方程组的总体GMERR算法[J].东北师大学报(自然科学版),2012,44(3):41-45. |
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| 作者姓名： | 郑玉晖 程东旭 钱晓惠 |
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| 作者单位： | 中原工学院理学院,河南郑州,450007 |
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| 基金项目： | 河南省重点科技攻关项目(082100210041);河南省自然科学基础研究计划项目(2007140020) |
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| 摘 要： | 提出求解具有多个右端项大规模非对称线性方程组AX=B的一个新方法.广义最小误差(GMERR)方法用于求解AX=B时,需要对每一个右端项分别求解,运算量大,并且求解一个线性方程组的信息不能有效的应用于另一个方程组.针对以上不足,将初始残量矩阵总体投影在一个Krylov子空间上,得到总体广义最小误差方法(总体GMERR方法)及相关性质.数值实验结果表明新方法比用GMERR算法分别求解每一个同系数矩阵而右端项不同的方程组更为有效.
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| 关 键 词： | Krylow子空间方法 多个右端项 线性方程组 总体GMERR算法 |
Global GMERR algorithm for linear systems with multiple right-hand sides |
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| ZHENG Yu-hui
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CHENG Dong-xu
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QIAN Xiao-hui.Global GMERR algorithm for linear systems with multiple right-hand sides[J].Journal of Northeast Normal University (Natural Science Edition),2012,44(3):41-45. |
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| Authors: | ZHENG Yu-hui CHENG Dong-xu QIAN Xiao-hui |
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| Institution: | (College of Science,Zhongyuan University of Technology,Zhengzhou 450007,China) |
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| Abstract: | A new algorithm for solving nonsymmetrical linear systems with multiple right-hand sides is given.The generalized minimal error method(GMERR method) may be used to solve large linear systems with multiple right-hand sides AX=B by solving each one separately.However,it is very expensive and the information of solving one linear system can not be used to solve another linear system.According to the deficiency,by projecting the initial residual matrix onto a matrix Krylov subspace,a new method-global generalized minimal error method(GLGMERR method) is presented.The numerical results show that this new algorithm is more effective than GMERR method. |
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| Keywords: | Krylov subspace method multiple right-hand sides linear systems global GMERR |
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