Fast solving of generalized Sylvester matrix equations $AX+YB=C$

In this presentation, we introduce a fast solving method for the generalized Sylvester equation $AX+YB=C$ using random projection. We focus specifically on the setting where the matrix $A$ is large and the matrix $B$ is small. In theoretical analysis, we derive a probabilistic upper bound for the residual of the solution obtained by the proposed method. Numerical experiments demonstrate that, compared to methods based on the Krylov subspace, our approach achieves solutions faster while maintaining a certain level of accuracy in the solutions. Temporary institution (from 09/2023) Laboratoire Jacques-Louis Lions, Sorbonne Université