| 史文谱,刘迎曦,褚京莲,郭淑红.求解线性方程组的一种新方法[J].计算力学学报,2003,20(6):715~720 |
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码上扫一扫！ |
| 求解线性方程组的一种新方法 |
| New method in solving linear system of equations |
| 修订日期：2002-06-12 |
| DOI：10.7511/jslx20036135 |
| 中文关键词: 一般系数矩阵 对称正定矩阵 良态线性方程组 病态线性方程组 系数矩阵 转置矩阵 |
| 英文关键词:general coefficient matrix,symmetric positive matrix,good-conditioned linear system of equations,ill-conditioned linear system of equations,variational problem,half-division optimization method |
| 基金项目:国家自然科学基金(10072014)，高校博士点专项基金(200001707)资助项目. |
| 史文谱 刘迎曦 褚京莲 郭淑红 |
[1]烟台大学机电(汽车)
工程学院，山东烟台264002 [2]大连理工大学工程力学系，辽宁大连116023 [3]烟台市技术学院基础系，山东烟台264002 |
| 摘要点击次数: 1564 |
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| 中文摘要: |
| 将线性方程组的一般系数矩阵转化为对称正定矩阵，从而把原线性方程组的求解问题转化为一个等价变分问题的极少值点寻优问题，借助对分寻优法进行求解。算例结果表明，本文方法不仅对于良态线性方程组的求解问题是有效的，而且对于病态线性方程组的求解问题同样是有效的。 |
| 英文摘要: |
| At the two sides of a system of linear equations, simultaneously left multiplying the conjugate matrix corresponding its coefficient matrix, the general coefficient matrix is changed into a symmetric positive one. Based on the variational principle, the solving problem for the original group of linear equation is transformed into an equivalent no constrained optimization programming. Then a half-division optimization method can be used to solve the problem. The results of the given examples prove that the method is effective for good-conditioned or ill-conditioned group of linear equations. Compared with the steepest descent method, Newton method and conjugate gradient method etc. show that the method provided has the following characteristics, such as wide suiting range, high convergence rate, high convergence precision, no beginning iteration point, simple algorithm, easy programming, strong ill conditioned-resistant. At last, the shortcomings of the method are also discussed. |
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