| 病态代数系统求解的精细迭代方法 |
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| 引用本文： | 张文志,黄培彦.病态代数系统求解的精细迭代方法[J].应用数学和力学,2013,34(7):736-741. |
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| 作者姓名： | 张文志 黄培彦 |
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| 作者单位： | 华南理工大学 土木与交通学院,广州 510640 |
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| 基金项目： | 国家自然科学基金(重点)资助项目 |
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| 摘 要： | 提出了病态代数系统求解的精细迭代方法．首先利用一个小参数对病态矩阵加以改良，将原病态系统的求解问题转化为该改良系统的求解问题．然后利用精细积分法给出了改良矩阵求逆的高精度方法．该方法具有高精度、高效率的优点，且对改良参数的适应性较好，具有良好的应用前景．理论和数值分析证明了该方法的有效性．
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| 关 键 词： | 病态代数系统 精细积分法 迭代算法 |
| 收稿时间： | 2013-05-20 |
Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations |
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| Institution: | School of Civil and Transportation Engineering, South China University of Technology, Guangzhou 510640, P.R.China |
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| Abstract: | A precise iterative refinement of solution for ill-conditioned systems of linear algebraic equations was proposed. First, the ill-conditioned matrix was improved through introduction of a small parametrr, and then via the precise integration method, a highly precise method was provided for the inversion of the improved matrix. Both the theoretical convergence analysis and numerical examples show the efficiency and accuracy of the method. |
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| Keywords: | ill-conditioned linear system precise integration method (PIM) iterative method |
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