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Recently, Tang et al. [Numer Algorithms. 2014;66(2):379-397] have offered a cyclic iterative method for determining the unique solution of the coupled matrix equations AiXBi = Fi, i = 1, 2,..., N. Analogues to the gradient-based algorithm, the proposed algorithm relies on a fixed parameter whereas it has wider convergence region. Nevertheless, the application of the algorithm to find the centrosymmetric solution of the mentioned problem has been left as a project to be investigated and the optimal value for the fixed parameter has not been derived. In this paper, we focus on a more general class of the coupled linear matrix equations that incorporate the mentioned ones in the earlier refereed work. More precisely, we first develop the authors' propounded algorithm to resolve our considered coupled linear matrix equations over centro-symmetric matrices. Afterwards, we disregard the restriction of the existence of the unique (centro-symmetric) solution and also modify the authors' algorithm by applying an oblique projection technique which allows to produce a sequence of approximate solutions which gratify an optimality property. Numerical results are reported to confirm the validity of the established results and to demonstrate the superior performance of the modified version of the cyclic iterative algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following minimization problem:where,,,andare given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal solution which is(R,S)-symmetric that minimize, and also satisfies the corrected matrix inequality constraint. A hybrid algorithm with convergence analysis is given to solve this problem. Numerical examples show that the algorithm requires less CPU times when compared with some other methods. [ABSTRACT FROM AUTHOR]