Solving coupled matrix equations over generalized bisymmetric matrices

Dehghan, Mehdi; Hajarian, Masoud

doi:10.1007/s12555-012-0506-2

Cited by 20 publications

(9 citation statements)

References 37 publications

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“…As is seen from this table, the number of iterations of L-GLS is less than that of the NSCG method. Dehghan and Hajarian (2012) and E, J, P, X * and Y * are the corresponding matrices in that example. We applied the L-GLS algorithm and Algorithm 1 of Dehghan and Hajarian (2012) (with a parameter m = 5.1141e25 that is used in Algorithm 1) for solving this example.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Dehghan and Hajarian (2012) and E, J, P, X * and Y * are the corresponding matrices in that example. We applied the L-GLS algorithm and Algorithm 1 of Dehghan and Hajarian (2012) (with a parameter m = 5.1141e25 that is used in Algorithm 1) for solving this example. Note that we select the best m from Dehghan and Hajarian (2012).…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…We applied the L-GLS algorithm and Algorithm 1 of Dehghan and Hajarian (2012) (with a parameter m = 5.1141e25 that is used in Algorithm 1) for solving this example. Note that we select the best m from Dehghan and Hajarian (2012). The numerical results are shown in Figure 3, with…”

Section: Numerical Experimentsmentioning

confidence: 99%

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A general iterative approach for solving the general constrained linear matrix equations system

Karimi

Dehghan

2015

Transactions of the Institute of Measurement and Control

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Much of the research which has been done on special kinds of matrix equations has almost the same structure. In this paper, an iterative approach is proposed which is more general and includes all such matrix equations. This approach is based on the global least squares (GL-LSQR) method. To do so, a linear matrix operator, its adjoint and a proper inner product are defined. Then we demonstrate how to employ the new approach for solving the general linear matrix equations system. When the matrix equations are consistent, a least-norm solution can be obtained. Moreover, the optimal approximate solution to a given group of matrices can be derived. Also, some theoretical properties and the error analysis of the new method are discussed. Finally, some numerical experiments are given to compare the new iterative method with some existent methods in terms of their numerical results and illustrate the efficiency of the new method.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

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A general iterative approach for solving the general constrained linear matrix equations system

Karimi

Dehghan

2015

Transactions of the Institute of Measurement and Control

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“…The general expressions of the ( R , S ) -symmetric and ( R , S ) -skew symmetric solutions were given in Dehghan and Hajarian (2011b). (Dehghan and Hajarian, 2010, 2012a, 2012b) obtained the solutions, the generalized bisymmetric solutions, the generalized centro-symmetric and central anti-symmetric solutions by extending the CGNE iterative method and GI method. Hajarian (2014) solved general coupled matrix equations by using the matrix form of the CGS method.…”

Section: Introductionmentioning

confidence: 99%

Finite iterative Hamiltonian solutions of the generalized coupled Sylvester – conjugate matrix equations

Bayoumi

2018

Transactions of the Institute of Measurement and Control

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In this paper, we present an iterative algorithm to solve a generalized coupled Sylvester – conjugate matrix equations over Hamiltonian matrices. When the considered systems of matrix equations are consistent, it is proven that the solution can be obtained within finite iterative steps for any arbitrary initial generalized Hamiltonian matrices in the absence of round off errors. Two numerical examples are given to illustrate the effectiveness of the proposed method.

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“…In order to improve the convergent rate of the GI method, two variants of the GI method were proposed to solve the Sylvester equations in [30,31]. Meanwhile, the GI method was extended to solve the common solutions, the generalized centro-symmetric solutions, generalized bisymmetric solutions, reflexive and anti-reflexive solutions of some coupled matrix equations, see [32][33][34][35][36] for further details on this topic. However, the optimal convergent factors of these extended GI methods were not given in computing such constraint solutions.…”

Section: Introductionmentioning

confidence: 99%

Iterative Hermitian R-conjugate solutions to general coupled sylvester matrix equations

2017

Filomat

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For a given symmetric orthogonal matrix R, i.e., RT = R, R2 = I, a matrix A ? Cnxn is termed Hermitian R-conjugate matrix if A = AH, RAR = ?. In this paper, an iterative method is constructed for finding the Hermitian R-conjugate solutions of general coupled Sylvester matrix equations. Convergence analysis shows that when the considered matrix equations have a unique solution group then the proposed method is always convergent for any initial Hermitian R-conjugate matrix group under a loose restriction on the convergent factor. Furthermore, the optimal convergent factor is derived. Finally, two numerical examples are given to demonstrate the theoretical results and effectiveness.

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Solving coupled matrix equations over generalized bisymmetric matrices

Cited by 20 publications

References 37 publications

A general iterative approach for solving the general constrained linear matrix equations system

A general iterative approach for solving the general constrained linear matrix equations system

Finite iterative Hamiltonian solutions of the generalized coupled Sylvester – conjugate matrix equations

Iterative Hermitian R-conjugate solutions to general coupled sylvester matrix equations

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