Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations. (English) Zbl 1446.65021
Summary: In this study, we consider the iteration solutions of the generalized coupled Sylvester-conjugate matrix equations: \(A_1 X + B_1 Y = D_1 \overline{X} E_1 + F_1\), \(A_2 Y + B_2 X = D_2 \overline{Y} E_2 + F_2\), where \(\overline{X}\) and \(\overline{Y}\) denote the conjugation of \(X\) and \(Y\), respectively. We propose a modified conjugate gradient method and give the convergence analysis based on the premise that the coupled matrix equations are consistent. The convergence theorem shows that a solution (\(X^*\), \(Y^*\)) can be obtained within finite iterative steps in the absence of round-off error for any initial value. Furthermore, we provide a method for choosing the initial matrices to obtain the minimum-norm solution of the problem. Finally, some numerical examples are given to demonstrate the behavior of the algorithms considered.
Keywords:
generalized coupled Sylvester-conjugate matrix equations; minimum-norm solution; modified conjugate gradient method; numerical experimentReferences:
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