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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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