A modified gradient based algorithm for solving matrix equations \(AXB+CX^T D=F\) (Q1714819)

Summary: In this paper, we develop a modified gradient based algorithm for solving matrix equations \(AXB+CX^T D=F\). Different from the gradient based method introduced by \textit{L. Xie} et al. [Appl. Math. Comput. 217, No. 5, 2191--2199 (2010; Zbl 1210.65097)] the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method.