<div dir="ltr"><p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:18pt;font-family:"Times New Roman",serif">SEMINARIO
DI MATEMATICA</span></p>
<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:10pt;font-family:"Times New Roman",serif"><span style="text-decoration-line:none"> </span></span></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span style="font-size:16pt;font-family:"Times New Roman",serif">venerdì 12 aprile 2019</span></b><b><span style="font-size:16pt;font-family:"Times New Roman",serif"></span></b></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">ore 11:00</span></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"> </span></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><u><span style="font-size:16pt;font-family:"Times New Roman",serif">Scuola Normale Superiore</span></u></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Pisa</span></p>
<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Aula Mancini</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><u><span style="font-size:10pt;font-family:"Times New Roman",serif"><span style="text-decoration-line:none"> </span></span></u></b></p>
<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span style="font-size:20pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">James Nagy</span></b><b><span style="font-size:20pt;font-family:"Times New Roman",serif"></span></b></p>
<h4 align="center" style="margin:0cm 0cm 0.0001pt;text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;break-after:avoid;font-size:12pt;font-family:Cambria,serif;color:rgb(79,129,189);font-style:italic"><span lang="EN-US" style="font-family:"Times New Roman",serif;color:windowtext;font-weight:normal;font-style:normal">(</span><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-weight:normal">Department of Mathematics, Emory University</span><span lang="EN-US" style="font-family:"Times New Roman",serif;color:windowtext;font-weight:normal;font-style:normal">)</span></h4>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span lang="EN-US" style="font-family:"Times New Roman",serif"> </span></i></p>
<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Terrà un
seminario dal titolo:</span></p>
<p align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;margin-right:0cm;margin-left:0cm;font-size:12pt;font-family:"Times New Roman",serif"><b><span lang="EN-US" style="font-size:18pt">“<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">MATLAB Tools for Large-Scale Linear
Inverse Problems</span></span></b><b><span lang="EN-US" style="font-size:18pt">”</span></b></p>
<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span lang="EN-US" style="font-family:"Times New Roman",serif"> </span></i></b></p>
<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-family:"Times New Roman",serif">Abstract:</span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-size:11pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Inverse problems arise
in a variety of applications: image processing,</span><span lang="EN-US" style="font-size:11pt;font-family:"Times New Roman",serif"> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">finance, mathematical
biology, and more. Mathematical models for these</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">applications may involve integral equations, partial differential</span>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">equations, and dynamical systems, and solution
schemes are formulated</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">by applying
algorithms that incorporate regularization techniques</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">and/or statistical approaches. In most cases these solutions
schemes</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">involve the need to solve a
large-scale ill-conditioned linear system</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">that
is corrupted by noise and other errors. In this talk we describe</span><br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">and demonstrate capabilities of a new MATLAB
software package that</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">consists of
state-of-the-art iterative methods for solving such</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">systems, which includes approaches that can
automatically estimate</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">regularization
parameters, stopping iterations, etc., making them very</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">simple to use. Thus, the package allows users to
easily incorporate</span><br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">into their own applications (or simply
experiment with) different</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">iterative
methods and regularization strategies with very little</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">programming effort. On the other hand,
sophisticated users can also</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">easily
access various options to tune the algorithms for certain</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">applications. Moreover, the package includes
several test problems</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">and examples to
illustrate how the iterative methods can be used on a</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">variety of large-scale inverse problems.</span><br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">The talk will begin with a brief introduction to
inverse problems,</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">discuss considerations
that are needed to compute an approximate</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">solution,
and describe some details about new efficient hybrid Krylov</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">subspace methods that are implemented in our package.
These methods</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">can guide users in
automatically choosing regularization parameters,</span><br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">and can be used to enforce various
regularization schemes, such as</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">sparsity.
We will use imaging examples that arise in medicine and</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">astronomy to illustrate the performance of the
methods.</span><br>
<br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">This is joint work with Silvia Gazzola
(University of Bath) and </span><br>
<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Per Christian Hansen (Technical University of
Denmark).</span></span><span lang="EN-US" style="font-size:11pt;font-family:"Times New Roman",serif"></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-size:11pt;font-family:"Times New Roman",serif"> </span></p><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div></div>
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