Optimality properties of Galerkin and Petrov-Galerkin methods for linear\n matrix equations

Galerkin and Petrov-Galerkin methods are some of the most successful solution\nprocedures in numerical analysis. Their popularity is mainly due to the\noptimality properties of their approximate solution. We show that these\nfeatures carry over to the (Petrov-)Galerkin methods applied for the solution\nof linear matrix equations. Some novel considerations about the use of Galerkin\nand Petrov-Galerkin schemes in the numerical treatment of general linear matrix\nequations are expounded and the use of constrained minimization techniques in\nthe Petrov-Galerkin framework is proposed.\n