We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium
and large scale, in case of rank-structured data, ie, when the coefficient matrices and the …

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important
role in various applications, including the stability analysis and dimensionality reduction of …

Can simple systems be regulated by simple controllers? Engineering experience indicates
that this is often the case. Certainly, the overwhelming majority of industrially deployed …

The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit
(LR-ADI) iteration are established numerical tools for computing low-rank solution factors of …

Many of the commonly used methods in model‐order reduction do not guarantee stability of
the reduced‐order model. This article extends the eigenvalue reassignment method of …

We focus on the problem of optimal control of large-scale systems whose models are
obtained by discretization of partial differential equations using the Finite Element (FE) or …

Given the matrix equation A X+ X B+ f (X) C= D in the unknown n× m matrix X, we analyze
existence and uniqueness conditions, together with computational solution strategies for f: R …

Some classes of nonlinear matrix equations, typically arising in queuing networks and
Markov chain applications, are presented from a theoretical and computational perspective …

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution
techniques exist for their generalized multiterm version, as they recently arose in stochastic …

We present methodologies for reduced order modeling of convection dominated flows.
Accordingly, three main problems are addressed. Firstly, an optimal manifold is realized to …