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CATEGORIES:Applied and Computational Analysis
SUMMARY:CANCELLED - Daniel Kressner (EPFL)
DTSTART;TZID=Europe/London:20231130T150000
DTEND;TZID=Europe/London:20231130T160000
UID:TALK207700AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/207700
DESCRIPTION:By a basic linear algebra result\, a family of two
or more commuting symmetric matrices has a common
eigenvector basis and can thus be jointly diagona
lized. Such joint eigenvalue problems come in seve
ral flavors and they play an important role in a v
ariety of applications\, including independent com
ponent analysis in signal processing\, multivariat
e polynomial systems\, tensor decompositions\, and
computational quantum chemistry. Perhaps surpris
ingly\, the development\nof robust numerical algor
ithms for solving such problems is by no means tri
vial. To start with\, roundoff error or other form
s of error will inevitably destroy commutativity a
ssumptions. In turn\, one can at best hope to find
approximate solutions to joint eigenvalue problem
s and\, in\nturn\, most existing approaches are ba
sed on optimization techniques\, which may or may
not recover the approximate solution. In this talk
\, we propose randomized methods that address join
t eigenvalue problems via the solution of one or a
few standard eigenvalue problems. The methods are
simple but surprisingly effective. We provide a t
heoretical explanation for their success by establ
ishing probabilistic guarantees for robust recover
y. Through numerical experiments on synthetic and
real-world data\, we show that our algorithms reac
h or outperform state-of-the-art optimization-base
d methods. This talk is based on joint work with H
aoze He.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Nicolas Boulle
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