| 解不定方程组的新方法 |
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| 引用本文： | 刘江瑞.解不定方程组的新方法[J].大连铁道学院学报,1988(4). |
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| 作者姓名： | 刘江瑞 |
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| 作者单位： | 大连铁道学院数学教研室 |
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| 摘 要： | 本文讨论了求解一类不定方程组的新方法,其系数矩阵形如其中K和(-H)为正定对称矩阵,应用平方根法分解K=UU~T以及S=UW~T,容易证明R=WW~T-H为正定对称的,进而分解R=VV~T,于是该方法具有平方根法的一切特点.最后对该方法进行了数值误差分析.
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| 关 键 词： | 正定矩阵 平方根法/正定对称矩阵 不定方程组 向后误差分析 |
A New Method Solving Indefinite Equation Systems |
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| Liu Jiangrui.A New Method Solving Indefinite Equation Systems[J].Journal of Dalian Railway Institute,1988(4). |
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| Authors: | Liu Jiangrui |
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| Institution: | Liu Jiangrui |
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| Abstract: | A new method solving a certain class of indefinite equation systems is discussed. The coefficient matrix of this systems is A. where A is formed of positive definite symmetric matrix K, (-H) and matrix S, S'. K= UU~r and S=UW~r are decomposed by using the quadratic root method. It is easily proved that R=WW-H is a positive definite symmetric, and R=VV~r is further decomposed. then A is formed of product of lower-triangular matrix, diagonal matrix and super-triangula marix. This method has all features of the quadratic root method. Finally,the error analysis of this method is given. |
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| Keywords: | positive definite matrix square root method/positive definte symmetric matrix indefinite equation system backward error analysis |
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