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SUMMARY:Michele Benzi (Scuola Normale Superiore Pisa\, Italy)
DTSTART:20200506T140000Z
DTEND:20200506T150000Z
DTSTAMP:20260423T022831Z
UID:E-NLA/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/E-NLA/3/">No
 nlocal dynamics on networks via fractional graph Laplacians: theory and nu
 merical methods</a>\nby Michele Benzi (Scuola Normale Superiore Pisa\, Ita
 ly) as part of E-NLA - Online seminar series on numerical linear algebra\n
 \n\nAbstract\nNonlocal diffusive dynamics on large\, sparse networks can b
 e modeled by means of systems of differential equations involving fraction
 al graph Laplacians. The solution of such systems leads to non-analytic ma
 trix functions\, due to the singularity of the graph Laplacian. Off-diagon
 al decay estimates for these and related matrix functions will be presente
 d\, together with explicit (closed form) expressions for some simple but i
 mportant examples. The case of directed networks (leading to nonsymmetric 
 Laplacians) will also be discussed.\n\nThe numerical approximation of the 
 dynamics can be implemented by means of Krylov subspace methods. The lack 
 of smoothness of the underlying function suggests the use of rational appr
 oximation techniques. Some results using a shift-and-invert approach will 
 be presented.\n\nApplications include the efficient exploration of large s
 patial networks and consensus dynamics in multi-agent systems.\n\nThis is 
 joint work with Daniele Bertaccini (U. of Rome `Tor Vergata’)\, Fabio Du
 rastante (IAC-CNR)\, and Igor Simunec (Scuola Normale Superiore).\n
LOCATION:https://researchseminars.org/talk/E-NLA/3/
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