Formulation and Solution of Matrix Algebraic Problems through Optimization Problems

In this chapter, taking into account the possibility to derive, by using a different computational paradigm, the open-loop balanced representation, some matrix computational methods are dealt with. The different computational methods are reformulated in terms of various optimization problems that can be addressed solving nonlinear matrix differential equations. This approach is appealing from a system point of view, in fact the formulation of a suitable optimization problem paves the way to a computational approach that is universal. From a numerical point of view, the solutions can be obtained using simple integration methods, such as the Euler method.