| 解病态线性代数方程组的常微分方程方法 |
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| 引用本文： | 吴新元. 解病态线性代数方程组的常微分方程方法[J]. 南京大学学报(自然科学版), 1993, 29(2): 195-199 |
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| 作者姓名： | 吴新元 |
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| 作者单位： | 南京大学数学系 |
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| 摘 要： | 本文提出用常微分方程方法构造解病态线性代数方程组的基本原理与数值方法,用本文构造的新算法在 BULL DPX/2360计算机上解1000阶以上的由 Hilbert 矩阵构成的严重病态线性代数方程组 HX=b,h_(ij)=i/(i j-1),b_i=1/i,即使采用单精度运算,解的相对精度仍具有五位有效数字.
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| 关 键 词： | 数值分析 常微分方程 线性方程组 |
THE METHOD OF ORDINARY DIFFERENTIAL EQUATIONS FOR SOLVING ILL-CONDITIONED LINEAR SYSTEM OF EQUATIONS |
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| WU Xingyuan. THE METHOD OF ORDINARY DIFFERENTIAL EQUATIONS FOR SOLVING ILL-CONDITIONED LINEAR SYSTEM OF EQUATIONS[J]. Journal of Nanjing University: Nat Sci Ed, 1993, 29(2): 195-199 |
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| Authors: | WU Xingyuan |
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| Affiliation: | Department of Mathematics |
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| Abstract: | For solving ill-conditioned system of equations,the fundmentals and algrithoms of using an ordinary differential equation method are put forward in this paper. The linear system of equations Hx=b with Hilbert coefficient matrix is solved by the new method on the computer BULL DPX2/2 360,where h_(ij)=1/(i j-1)and b_i=1/i for i=1,2,...,1000,j=1,2,...,1000.The relative precision of the numerical solutions has 5 significant digits even though using single precision. |
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| Keywords: | mumerical analysis ordinary differential equations system of linear equations |
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