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 …

This paper presents a general framework for solving the low-rank and/or sparse matrix
minimization problems, which may involve multiple nonsmooth terms. The iteratively …

We consider large linear systems arising from the isogeometric discretization of the Poisson
problem on a single-patch domain. The numerical solution of such systems is considered a …

This work is an updated edition of my self-published monograph on The ADI Model Problem
[Wachspress, 1995]. Minor typographic corrections have been made in Chaps. 1–4. A few …

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 …

The global (patch-wise) geometry map, which describes the computational domain, is a new
feature in isogeometric analysis. This map has a global tensor structure, inherited from the …

In this paper, we study possible low rank solution methods for generalized Lyapunov
equations arising in bilinear and stochastic control. We show that under certain assumptions …

The differential Sylvester equation and its symmetric version, the differential Lyapunov
equation, appear in different fields of applied mathematics like control theory, system theory …

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in
molecular simulations, high-order correlation functions, and optimization. In this paper, we …