On the generalized ADI method for the matrix equation \(X- AXB\)=\(C\)
The authors consider the generalized alternating direction implicit (ADI) iterative method for solving the matrix equation \(X-AXB=C\). For analysing the convergence of the iterative method a corresponding rational approximation problem is formulated and investigated. A theory on the characterization and uniqueness of the optimal solution is presented. A Remes like algorithm for the computation of that solution is described and its convergence is proved. Finally, numerical experiments are reported.
alternating direction implicit iterative method
scientific article; zbMATH DE number 1961622