| 加权广义逆矩阵的迭代算法 |
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| 引用本文： | 史晓发,乔彦臣.加权广义逆矩阵的迭代算法[J].大连理工大学学报,1988(4). |
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| 作者姓名： | 史晓发 乔彦臣 |
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| 作者单位： | 大连理工大学应用数学系，大连轻工业学院 |
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| 摘 要： | 简要讨论了加权Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ广义逆矩阵的一些基本性质：给出了计算加权Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ广义逆矩阵的四种迭代算法，其中两种为线性算法，另外两种为高阶算法：讨论了诸算法间的相互关系，给出了高阶算法的一种较好的初始矩阵；讨论了诸算法的收敛性条件，给出了最佳的迭代参数；最后．讨论了算法在求解加权最小二乘问题中的应用。
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| 关 键 词： | 加权 广义逆 迭代法 参数/初始矩阵 |
Iterative Methods for Computing Weighted Moore-Penrose Inverses of Matrices |
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| Shi Xiaofa,Qiao Yanchen.Iterative Methods for Computing Weighted Moore-Penrose Inverses of Matrices[J].Journal of Dalian University of Technology,1988(4). |
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| Authors: | Shi Xiaofa Qiao Yanchen |
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| Abstract: | Some basic properties of weighted Moore-Penrose inverses of matrices are discussed. Two linear iterative methods and two hyperpower iterative methods for the computations of weighted Moore-Penrose generalized inverses of matrices are given. The convergence theorem of these methods is given.The relationship among these methods is discussed. Finally, one method is applied to solving the weighted least squares problem. |
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| Keywords: | weighted generalized in verse (matrix) iteration method parameter/initial matrix |
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