| 高阶满阵线性代数方程组的快速解法及其应用研究 |
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| 引用本文： | 张宗斌,高正红.高阶满阵线性代数方程组的快速解法及其应用研究[J].空气动力学学报,2005,23(3):365-369. |
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| 作者姓名： | 张宗斌 高正红 |
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| 作者单位： | 西北工业大学,陕西,西安,710072;成都飞机设计研究所,四川,成都,610041;西北工业大学,陕西,西安,710072 |
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| 摘 要： | 在非对称、非正定满阵线性方程组的求解过程中,本文以高斯迭代为基础,提出一种残差优化的迭代法.该法在迭代收敛过程中,残差单调下降,大大缩短了线性方程组的求解时间.用该法替代直接解法,增大了求解方程组的阶数,缩短了计算周期,对复杂飞行器气动、隐身一体化优化设计具有重要的工程价值.该方法还可以广泛地推广到其它应用领域.
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| 关 键 词： | 线性方程组 面元法 残差优化 |
| 文章编号： | 0258-1825（2005）03-365-05 |
| 收稿时间： | 2004-06-07 |
| 修稿时间： | 2004-06-072004-08-17 |
The rapid solution and application research of higher order nonsparse coefficient matrix linear equation system |
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| ZHANG Zong-bin,GAO Zheng-hong.The rapid solution and application research of higher order nonsparse coefficient matrix linear equation system[J].Acta Aerodynamica Sinica,2005,23(3):365-369. |
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| Authors: | ZHANG Zong-bin GAO Zheng-hong |
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| Abstract: | To solve linear equation system with an asymmetric, nonpositive-definition and nonsparse coefficient matrix, a residual minimization method based on Gaussian iteration is proposed in this paper. By using the method, a rapid and monotone reduction of the residual could be achieved and the optimization efficiency could be increased for a design problem. The results of the demonstration problem shows the feasibility and applicability of the method. |
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| Keywords: | linear equation system panel method residual minimization |
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