| 长方矩阵加权群逆的迭代法 |
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| 引用本文： | 胡春梅,刘晓冀.长方矩阵加权群逆的迭代法[J].高等学校计算数学学报,2012,34(1):16-22. |
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| 作者姓名： | 胡春梅 刘晓冀 |
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| 作者单位： | 1. 丽江师范高等专科学校数理系,丽江,674100
2. 广西民族大学数学与计算机科学学院,南宁,530006 |
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| 基金项目： | 国家自然科学基金，教育部科技重点项目 |
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| 摘 要： | 1引 言与引理
最近,文1]定义了长方矩阵的一种加权群逆:设A∈Cm×n,W∈Cn×m.称满足下列矩阵方程组的矩阵X∈Cm×n为A的加W权群逆:(W1)AWXWA=A, (W2)XWAWX=X, (W3)AWX=XWA通常记A的加W权群逆为A#W.若A#W存在,则它是唯一的.
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| 关 键 词： | rectangular matrix weighted group inverse iterative method |
ITERATIVE METHODS FOR THE WEIGHTED GROUP INVERSES OF RECTANGULAR MATRICES |
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| Hu Chunmei
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Liu Chunme.ITERATIVE METHODS FOR THE WEIGHTED GROUP INVERSES OF RECTANGULAR MATRICES[J].Numerical Mathematics A Journal of Chinese Universities,2012,34(1):16-22. |
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| Authors: | Hu Chunmei Liu Chunme |
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| Institution: | (College of Maths and Computer Science,Guangxi University for Nationalities,Nanning 530006) |
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| Abstract: | Cen has defined a weighted group inverse of rectangular matrices.Let A∈Cm×n,W∈Cn×m,X∈C,×n is called the weighted group inverse of A with W if it satisfies the system of matrix equations: （W1）AWXWA = A,（W2）XWAWX = X,（W3）AWX = XWA, and denoted by AW#.In this paper,we establish three iteration methods for computing the weighted group inverses of rectangular matrices,and prove the necessary and sufficient conditions for the convergence of the iterations.A numerical example is shown for illustration. |
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| Keywords: | rectangular matrix weighted group inverse iterative method |
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