<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Buongiorno a tutti. <div class=""><br class=""></div><div class="">trasmetto a tutti gli interessati l'invito al seminario del Prof. Michele Benzi, il 18/11/2022 alle ore 14:00 presso l'Aula Scarpa dell'Universita` di Pavia.</div><div class=""><br class=""></div><div class=""><div class="">Un saluto cordiale Giancarlo Sangalli</div><div class=""><br class=""></div><div class=""><div><blockquote type="cite" class=""><div class=""></div></blockquote></div></div></div><div class="">*******************************************************************************************************************************************</div><div class=""><span class="" style="line-height: 16px;"><font size="4" face="Times" class="">Functions of matrices: theory, applications and computation</font></span><div class="" style="line-height: 16px;"><font size="4" face="Times" class=""><br class=""></font></div><div class="" style="line-height: 16px;"><font size="4" face="Times" class="">Michele Benzi</font></div><div class="" style="line-height: 16px;"><font size="4" face="Times" class="">Scuola Normale Superiore, Pisa<br class=""></font><div class=""><font size="4" face="Times" class=""><br class=""></font></div><div class=""><font size="4" face="Times" class="">Abstract: In this talk I will first give a brief history of matrix and operator functions. </font></div><div class=""><font size="4" face="Times" class="">The story begins with the early work of Cayley and Sylvester on matrix algebra in the</font></div><div class=""><font size="4" face="Times" class="">XIX Century, continues in the XX Century with the important contributions of Weyr, </font></div><div class=""><font size="4" face="Times" class="">E. Cartan, Giorgi, and Cipolla, and culminates with the development of various functional </font></div><div class=""><font size="4" face="Times" class="">calculi for linear operators (both bounded and unbounded) in the context of modern </font></div><div class=""><font size="4" face="Times" class="">functional analysis. Much of this work is motivated by applications, especially in Physics,</font></div><div class=""><font size="4" face="Times" class="">a few of which will be described in the second part of the talk, together with emerging </font></div><div class=""><font size="4" face="Times" class="">new applications in Network Science. In the last part of the talk I will discuss some results </font></div><div class=""><font size="4" face="Times" class="">on decay properties of functions of large, sparse matrices and current work on efficient </font></div><div class=""><font size="4" face="Times" class="">algorithms for evaluating quantities such as the trace of a matrix function or the action of </font></div><div class=""><font size="4" face="Times" class="">a matrix function on a given vector using Krylov subspace methods. </font></div></div></div><div class=""><div class="">*******************************************************************************************************************************************</div></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div><blockquote type="cite" class=""><div class=""><div class=""><br class=""></div></div></blockquote></div></div></body></html>