Questo sito utilizza solo cookie tecnici per il corretto funzionamento delle pagine web e per il miglioramento dei servizi.
Se vuoi saperne di più o negare il consenso consulta l'informativa sulla privacy.
Proseguendo la navigazione del sito acconsenti all'uso dei cookie.
Se vuoi saperne di più o negare il consenso consulta l'informativa sulla privacy.
Proseguendo la navigazione del sito acconsenti all'uso dei cookie.
Seminario del 2022
2022
10 maggio
Valeria Simoncini
nell'ambito della serie: TOPICS IN MATHEMATICS 2021/2022
Seminario di analisi numerica
The numerical solution of possibly large dimensional algebraic linear systems permeates scientific modelling.
Often systems with multiple right-hand sides arise, whose efficient numerical solution usually requires ad-hoc procedures.
In the past decades a new class of linear equations has shown to be the natural algebraic framework in the discretization of
mathematical models in a variety of scientific applications. These problems are given by multiterm linear matrix equations of the form
A_1 X B_1 + A_2 X B_2 + ... + A_k X B_k = C
where all appearing terms are matrices of conforming dimensions, and X is an unknown matrix.
The case k=2 is called the Sylvester equation, and computational methods for its solution are well established, especially for small dimensions. The general multiterm case turns out to be a key ingredient in problems such as time-space, stochastic and parametric partial differential equations. Its numerical solution is the current challenge, though little
is known also about its algebraic properties.
In this lecture we give a gentle introduction to the problem, and discuss various attempts to numerically solve it.