The solvability conditions for the inverse eigenproblems of symmetric and generalized centro-symmetric matrices and their approximations
| Autor: | Yan-ping Sheng, Dongxiu Xie, Xi-Yan Hu |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Pure mathematics
Numerical Analysis Algebra and Number Theory Mathematical analysis Matrix norm Inverse The optimal approximation Expression (computer science) Inverse problem Matrix (mathematics) Inverse eigenproblem Symmetric matrix Discrete Mathematics and Combinatorics Geometry and Topology Element (category theory) Normed vector space Mathematics |
| Zdroj: | Linear Algebra and its Applications. 418(1):142-152 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2006.01.027 |
| Popis: | Let ∥ · ∥ be the Frobenius norm of matrices. We consider (I) the set SE of symmetric and generalized centro-symmetric real n × n matrices Rn with some given eigenpairs (λj, qj) (j = 1, 2, … , m) and (II) the element Rˆ in SE which minimizes ‖R∗-Rˆ‖ for a given real matrix R∗. Necessary and sufficient conditions for SE to be nonempty are presented. A general form of elements in SE is given and an explicit expression of the minimizer Rˆ is derived. Finally, a numerical example is reported. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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