5 papers
A low-rank matrix equation method for solving PDE-constrained optimization problems
Alexandra Bünger, Valeria Simoncini, Martin Stoll
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization pro…
Matrix oriented reduction of space-time Petrov-Galerkin variational problems
Julian Henning, Davide Palitta, Valeria Simoncini +1
Variational formulations of time-dependent PDEs in space and time yield -dimensional problems to be solved numerically. This increases the number of unknowns as well as the…
Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations
Davide Palitta, Valeria Simoncini
Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their…
Order reduction methods for solving large-scale differential matrix Riccati equations
Gerhard Kirsten, Valeria Simoncini
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen…
On the existence and approximation of a dissipating feedback
Nicola Guglielmi, Valeria Simoncini
Given a matrix and a tall rectangular matrix , , we consider the problem of making the pair dissipative, that is the dete…