Numerical simulation of large-scale dynamical systems plays a fundamental role in studying
a wide range of complex physical phenomena; however, the inherent large-scale nature of …

Efficient numerical algorithms for the solution of large and sparse matrix Riccati and
Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have …

Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

In this paper, we investigate a recently introduced approach for nonlinear model order
reduction based on generalized moment matching. Using basic tensor calculus, we propose …

In this paper, we discuss the model order reduction problem for descriptor systems, that is,
systems with dynamics described by differential-algebraic equations. We focus on linear …

In this work we obtain closed-form expression for the solution of non-symmetric algebraic
Riccati equation (NARE), A X+ X B+ XCX= D, A, B, C, D∈ ℂ n× n, under some conditions on …

Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well
established methods for the numerical solution of large-scale Sylvester and Lyapunov …

In this article a boundary feedback stabilization approach for incompressible Navier--Stokes
flows is studied. One of the main difficulties encountered is the fact that after space …

We consider balanced truncation model order reduction for symmetric second-order
systems. The occurring large-scale generalized and structured Lyapunov equations are …

We propose efficient algorithms for solving large-scale matrix differential equations. In
particular, we deal with the differential Riccati equations (DRE) and state the applicability to …