| 特殊五对角与七对角对称正定矩阵的一类反问题 |
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| 引用本文： | 邓远北,文亚云.特殊五对角与七对角对称正定矩阵的一类反问题[J].计算数学,2018,40(3):241-253. |
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| 作者姓名： | 邓远北 文亚云 |
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| 作者单位： | 湖南大学数学与计量经济学院, 长沙 410082 |
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| 摘 要： | 针对线性代数方程组Ax=b,利用矩阵分解的思想,构造一类特殊五对角与七对角对称正定阵的矩阵分解,获得这类矩阵反问题解存在的充要条件和通解表达式.最后,给出了具体算法与数值算例.
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| 关 键 词： | 线性代数方程组 矩阵分解 对称正定阵 反问题 |
INVERSE PROBLEMS FOR FIVE AND SEVEN DIAGONAL SYMMETRIC POSITIVE DEFINITE MATRICES |
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| Deng Yuanbei,Wen Yayun.INVERSE PROBLEMS FOR FIVE AND SEVEN DIAGONAL SYMMETRIC POSITIVE DEFINITE MATRICES[J].Mathematica Numerica Sinica,2018,40(3):241-253. |
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| Authors: | Deng Yuanbei Wen Yayun |
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| Institution: | College of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
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| Abstract: | According to the system of linear algebraic equations Ax=b,this paper uses the matrix decomposition to construct a kind of special five and seven diagonal matrix decomposition of symmetric positive definite matrices,and it gives a sufficient and necessary condition for the existence of solution for inverse problems of the matrices and the general representation.Finally,the algorithm and example are given. |
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| Keywords: | the system of linear algebraic equations the matrix decomposition symmetric positive definite matrices inverse problems |
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