The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Dongxiu Xie Xiyan Hu

Institution:	^a Beijing Institute of Machinery Industry, Beijing 100085, China ^b Department of Applied Mathematics, Hunan University, Changsha 410082, China

Abstract:	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.

Keywords:	Matrix norm Inverse eigenproblem The optimal approximation
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