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 …

This monograph aims to provide a concise and comprehensive treatment of the basic theory
of algebraic Riccati equations and a description of both the classical and the more advanced …

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 …

For large scale problems, an effective approach for solving the algebraic Lyapunov equation
consists of projecting the problem onto a significantly smaller space and then solving the …

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 …

The solution of large-scale Lyapunov equations is a crucial problem for several fields of
modern applied mathematics. The low-rank Cholesky factor version of the alternating …

In the numerical solution of the algebraic Riccati equation A^*X+XA-XBB^*X+C^*C=0,
where A is large, sparse, and stable, and B, C have low rank, projection methods have …

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 …