An iterative algorithm for solving a pair of matrix equations over generalized centro-symmetric matrices |
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Authors: | Mehdi Dehghan Masoud Hajarian |
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Affiliation: | aDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran 15914, Iran |
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Abstract: | A matrix is said to be a symmetric orthogonal matrix if . A matrix is said to be generalized centro-symmetric (generalized central anti-symmetric) with respect to P, if A=PAP (A=−PAP). The generalized centro-symmetric matrices have wide applications in information theory, linear estimate theory and numerical analysis. In this paper, we propose a new iterative algorithm to compute a generalized centro-symmetric solution of the linear matrix equations . We show, when the matrix equations are consistent over generalized centro-symmetric matrix Y, for any initial generalized centro-symmetric matrix Y1, the sequence {Yk} generated by the introduced algorithm converges to a generalized centro-symmetric solution of matrix equations . The least Frobenius norm generalized centro-symmetric solution can be derived when a special initial generalized centro-symmetric matrix is chosen. Furthermore, the optimal approximation generalized centro-symmetric solution to a given generalized centro-symmetric matrix can be derived. Several numerical examples are given to show the efficiency of the presented method. |
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Keywords: | Matrix equations Iterative method Generalized centro-symmetric matrix Least Frobenius norm generalized centro-symmetric solution Symmetric orthogonal matrix |
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