# Computational methods for large-scale matrix equations and application to PDEs

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3786

dept.math [at] unitn.it

**Luogo:** Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"**Ore**: 16:30

**Relatrice:**Valeria Simoncini (Dipartimento di Matematica Università di Bologna)

**Abstract: **

Linear matrix equations such as the Lyapunov and Sylvester equations and their generalizations have classically played an important role in the analysis of dynamical systems, in control theory and in eigenvalue computation. More recently, matrix equations have emerged as a atural linear algebra framework for the discretized version of (systems of) deterministic and stochastic partial differential equations ((S)PDEs), and new challenges have arisen.

In this talk we will review some of the key methodologies for solving large scale linear matrix equations. We will also discuss recent strategies for the numerical solution of more involved equations, such as multiterm linear matrix equations and bilinear systems of equations, which are currently attracting great interest due to their occurrence in new application models associated with (S)PDEs.

**Referenti: **Ana Maria Alonso Rodriguez - Eduardo Luis Sola Conde