| k次R-对称矩阵的特征值反问题及最佳逼近问题 |
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| 引用本文： | 贾志刚,魏木生. k次R-对称矩阵的特征值反问题及最佳逼近问题[J]. 高等学校计算数学学报, 2010, 32(1) |
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| 作者姓名： | 贾志刚 魏木生 |
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| 作者单位： | 1. 徐州师范大学数学科学学院,徐州,221116
2. 上海师范大学数学系,上海市高校科学计算重点实验室,上海200234 |
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| 摘 要： | <正>1引言在[7]中,Trench推广了中心对称矩阵和自反矩阵的概念定义了R-对称矩阵,采用一个统一的方式证明了许多已有的结论并得到更强的结果.在Trench工作的基础上,文[6]定义了k次R-对称矩阵,并指出对于任意奇异的Hermitian矩阵A,都存在k次单位矩阵R
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| 关 键 词： | 线性无关 特征向量 逼近问题 矩阵特征值 中心对称矩阵 最佳逼近 对称解 特征值反问题 |
k DEGREE R-SYMMETRIC INVERSE PROBLEM AND ITS OPTIMAL APPROXIMATION PROBLEM |
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| Jia Zhigang Wei Musheng. k DEGREE R-SYMMETRIC INVERSE PROBLEM AND ITS OPTIMAL APPROXIMATION PROBLEM[J]. Numerical Mathematics A Journal of Chinese Universities, 2010, 32(1) |
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| Authors: | Jia Zhigang Wei Musheng |
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| Affiliation: | Jia Zhigang (School of Mathematical Sciences,Xuzhou Normal University,Xuzhou 221116) Wei Musheng (Department of Mathematics,Shanghai Normal University,Scientific Computing Key Laboratory of Shanghai Universities,Shanghai 200234) |
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| Abstract: | The k degree R-symmetric inverse eigenvalue problem as well as corresponding optimal approximation problem is studied in this paper.A sufficient condition for the existence of a k degree R-symmetric solution is that the given eigenvectors are of special structures.We character such structures and present the general forms of solutions for these two problems. |
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| Keywords: | k degree R-symmetric matrix inverse eigenvalue problem optimal approximation |
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