On the Solvability of a System of Matrix Equations AX = B and BY = A Over Associative Rings

2019 ◽  
Vol 238 (1) ◽  
pp. 22-31
Author(s):  
V. M. Prokip
Keyword(s):  
Matrix Equations ◽  
System Of Matrix Equations ◽  
Associative Rings

A system of matrix equations and its applications

2013 ◽  
Vol 56 (9) ◽  
pp. 1795-1820 ◽  
Author(s):  
QingWen Wang ◽  
ZhuoHeng He
Keyword(s):  
Matrix Equations ◽  
System Of Matrix Equations

A System of Matrix Equations over the Quaternion Algebra with Applications

2017 ◽  
Vol 24 (02) ◽  
pp. 233-253 ◽  
Author(s):  
Xiangrong Nie ◽  
Qingwen Wang ◽  
Yang Zhang
Keyword(s):  
General Solution ◽  
Quaternion Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Equations ◽  
Electronic Networks ◽  
Consistency Conditions ◽  
Numerical Example ◽  
System Of Matrix Equations ◽  
Necessary And Sufficient

We in this paper give necessary and sufficient conditions for the existence of the general solution to the system of matrix equations [Formula: see text] and [Formula: see text] over the quaternion algebra ℍ, and present an expression of the general solution to this system when it is solvable. Using the results, we give some necessary and sufficient conditions for the system of matrix equations [Formula: see text] over ℍ to have a reducible solution as well as the representation of such solution to the system when the consistency conditions are met. A numerical example is also given to illustrate our results. As another application, we give the necessary and sufficient conditions for two associated electronic networks to have the same branch current and branch voltage and give the expressions of the same branch current and branch voltage when the conditions are satisfied.

A system of matrix equations with five variables

2015 ◽  
Vol 271 ◽  
pp. 805-819 ◽  
Author(s):  
Abdur Rehman ◽  
Qing-Wen Wang
Keyword(s):  
Matrix Equations ◽  
System Of Matrix Equations

AN APPLICATION OF QUADRUPLE FIXED POINT THEOREMS TO A NONLINEAR SYSTEM OF MATRIX EQUATIONS

2018 ◽  
Vol 103 (3) ◽  
pp. 659-669 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Waleed Khalid Abduljabbar ◽  
Abdu Mohammed Ali Atta ◽  
Sokhobiddin Akhatkulov
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorems ◽  
Matrix Equations ◽  
System Of Matrix Equations ◽  
Quadruple Fixed Point

Delayed over-relaxation in iterative schemes to solve rank deficient linear system of (matrix) equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3181-3198
Author(s):  
Arezo Ameri ◽  
Fatemeh Beik
Keyword(s):  
Linear System ◽  
Coefficient Matrix ◽  
System Of Equations ◽  
Matrix Equations ◽  
Linear System Of Equations ◽  
System Of Matrix Equations ◽  
Gradient Based ◽  
Richardson Method ◽  
Singular Linear System ◽  
Symmetric Systems

Recently in [Journal of Computational Physics, 321 (2016), 829-907], an approach has been developed for solving linear system of equations with nonsingular coefficient matrix. The method is derived by using a delayed over-relaxation step (DORS) in a generic (convergent) basic stationary iterative method. In this paper, we first prove semi-convergence of iterative methods with DORS to solve singular linear system of equations. In particular, we propose applying the DORS in the Modified HSS (MHSS) to solve singular complex symmetric systems and in the Richardson method to solve normal equations. Moreover, based on the obtained results, an algorithm is developed for solving coupled matrix equations. It is seen that the proposed method outperforms the relaxed gradient-based (RGB) method [Comput. Math. Appl. 74 (2017), no. 3, 597-604] for solving coupled matrix equations. Numerical results are examined to illustrate the validity of the established results and applicability of the presented algorithms.

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