The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations. (English) Zbl 1350.65036
Summary: In this paper, we consider the iteration solutions of generalized coupled Sylvester-transpose matrix equations: \(A_1XB_1+C_1Y^TD_1=F_1\), \(A_2YB_2+C_2X^TD_2=F_2\). When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a solution \((X^\ast,Y^\ast)\) can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the minimum-norm solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares solution with the minimum-norm. Finally, some numerical examples are given to show the behavior of the considered algorithms.
MSC:
| 65F30 | Other matrix algorithms (MSC2010) |
| 65F10 | Iterative numerical methods for linear systems |
| 15A24 | Matrix equations and identities |
Keywords:
generalized coupled Sylvester-transpose matrix equations; modified conjugate gradient method; minimum-norm solution; least squares solution; numerical experimentReferences:
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