The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations

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• 作者：Dongxiu Xie ; Xiyan Hu and Yan-ping Sheng
• 关键词：Matrix norm ; Inverse eigenproblem ; The optimal approximation
• 刊名：Linear Algebra and its Applications
• 出版年：2006
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 October 2006
• 卷：418
• 期：1
• 页码：142-152
• 文件大小：154 K

摘要

Let · be the Frobenius norm of matrices. We consider (I) the set S_E of symmetric and generalized centro-symmetric real n × n matrices R_n with some given eigenpairs (λ_j, q_j) (j = 1, 2, … , m) and (II) the element in S_E which minimizes for a given real matrix R^*. Necessary and sufficient conditions for S_E to be nonempty are presented. A general form of elements in S_E is given and an explicit expression of the minimizer is derived. Finally, a numerical example is reported.