Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/37920

 Title: Minimization problems for certain structured matrices Author(s): Zhongyun LiuRalha, RuiZhang, YulinFerreira, Carla Keywords: Least-squares approximationCentralizer of JMoore- Penrose inverseAnticentralizer of J Issue date: Oct-2015 Publisher: International Linear Algebra Society Journal: Electronic Journal of Linear Algebra Abstract(s): For given $Z,B\in \mathbb{ C}^{n\times k}$, the problem of finding $A\in \mathbb{C}^{n\times n}$, in some prescribed class ${\cal W}$, that minimizes $\|AZ-B\|$ (Frobenius norm) has been considered by different authors for distinct classes ${\cal W}$. Here, we study this minimization problem for two other classes which include the symmetric Hamiltonian, symmetric skew-Hamiltonian, real orthogonal symplectic and unitary conjugate symplectic matrices. We also consider (as others have done for other classes ${\cal W}$) the problem of minimizing $\|A-\tilde{A}\|$ where $\tilde{A}$ is given and $A$ is a solution of the previous problem. The key idea of our contribution is the reduction of each one of the above minimization problems to two independent subproblems in orthogonal subspaces of $\mathbb{C}^{n\times n}$. This is possible due to the special structures under consideration. We have developed MATLAB codes and present the numerical results of some tests. Type: Article URI: http://hdl.handle.net/1822/37920 DOI: 10.13001/1081-3810.3144 ISSN: 1081-3810 Publisher version: http://repository.uwyo.edu/ela/ Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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