| 求解病态线性方程组的混合算法 |
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| 引用本文： | 郑洲顺,黄光辉,杨晓辉.求解病态线性方程组的混合算法[J].贵州工业大学学报(自然科学版),2008,37(3). |
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| 作者姓名： | 郑洲顺 黄光辉 杨晓辉 |
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| 作者单位： | 中南大学数学科学与计算技术学院,湖南长沙,410083 |
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| 基金项目： | 国家高技术研究发展计划(863计划)，中南大学校科研和教改项目，中南大学创新基金，国家大学生创新性实验计划立项项目 |
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| 摘 要： | 首先通过变分原理将求解线性方程组的问题转化为等价的求解无约束函数最优化问题的极小值.通过研究BFGS算法和模拟退火算法的优缺点,鉴于BFGS的良好的局部搜索能力以及模拟退火法的全局搜索能力,提出了一个BFGs-SA的混合算法.数值实验表明该混合算法校正了BFGS的局部搜索能力,达到了全局最优解,从而得到了原病态线性方程组的解.
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| 关 键 词： | BFGS算法 模拟退火算法 全局优化 混合算法 病态线性方程组 |
A Mixed Algortithm for Solving Ill-Conditioned Linear Equations |
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| ZHENG Zhou-shun,HUANG Guang-hui,YANG Xiao-hui.A Mixed Algortithm for Solving Ill-Conditioned Linear Equations[J].Journal of Guizhou University of Technology(Natural Science Edition),2008,37(3). |
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| Authors: | ZHENG Zhou-shun HUANG Guang-hui YANG Xiao-hui |
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| Institution: | ZHENG Zhou-shun,HUANG Guang-hui,YANG Xiao-hui (School of Mathematical Science , Computing Technology,Central South University,Changsha 410012,China) |
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| Abstract: | The problem of solving linear equations changed equivalently into the problem of searching the minimum of unconstrained optimizations of function by variation principle in the paper.The advantages and disadvantages of BFGS algorithm and simulated annealing algorithm were studied and considering BFGS's good local searching ability and simulated annealing algorithm' global searching ability,a mixed BFGS-SA algorithm was proposed in the paper.Numerical experiments show the mixed algorithm corrects the BFGS' lo... |
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| Keywords: | BFGS algorithm simulated annealing algorithm global optimization mixed algorithm ill-conditioned linear equations |
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