| 一类子矩阵约束下矩阵反问题的拓广 |
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| 引用本文： | 熊培银,周富照,祝志栋. 一类子矩阵约束下矩阵反问题的拓广[J]. 贵州大学学报(自然科学版), 2009, 26(6): 17-20 |
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| 作者姓名： | 熊培银 周富照 祝志栋 |
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| 作者单位： | 仰恩大学,数学系,福建,泉州,362014;长沙理工大学,数计学院,湖南,长沙,410076 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 利用矩阵的广义逆和广义奇异值分解，讨论了子矩阵约束下左右逆特征值问题及其拓广，给出了其有解的充分必要条件及在有解条件下的通解表达式，并得到了此问题的最佳逼近解，而且用数值算法来验证求最佳逼近解的有效性．
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| 关 键 词： | 矩阵扩充 左右逆特征值问题 广义奇异值分解 最佳逼近 |
A Generalization of a Class of Inverse Problem for Matrices with a Submatrix |
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| XIONG Pei-yin,ZHOU Fu-zhao,ZHU Zhi-dong. A Generalization of a Class of Inverse Problem for Matrices with a Submatrix[J]. Journal of Guizhou University(Natural Science), 2009, 26(6): 17-20 |
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| Authors: | XIONG Pei-yin ZHOU Fu-zhao ZHU Zhi-dong |
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| Affiliation: | XIONG Pei-yin, ZHOU Fu-zhao, ZHU Zhi-dong (1. Department of Mathematics, Yang-En College, Quanzhou 362014,China; 2. College of Mathematics and Computational Science ,Changsha University of Science ＆ Technology , Changsha 410076,China) |
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| Abstract: | By the generalized inverse and the generalized singular-value decomposition, the problem of left and right inverse eigenvalue with a submatrix was studied, In addition, the sufficient and necessary conditions and the general solutions of the problem were given, and the optimal approximate solution was obtained. Numeral algorithm was given to show the effectiveness of the proposed method. |
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| Keywords: | the expansion of matrices left and fight inverse eigenvalue problems generalized singular-value decomposition optimal approximation |
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