Recursive blocked algorithms for linear systems with Kronecker product structure
Provides a more efficient numerical method for solving linear systems with Kronecker product structure, benefiting applications in PDE discretization and macroeconomics.
The paper extends recursive blocked algorithms to solve higher-dimensional generalized Sylvester matrix equations, achieving superior efficiency compared to existing Sylvester-based solvers.
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of generalized Sylvester matrix equations, as they arise from the discretization of PDEs with separable coefficients or the approximation of certain models in macroeconomics. By combining recursions with a mechanism for merging dimensions, an efficient algorithm is derived that outperforms existing approaches based on Sylvester solvers.