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SUMMARY:CANCELLED - Daniel Kressner (EPFL)
DTSTART:20231130T150000Z
DTEND:20231130T160000Z
UID:TALK207700@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:By a basic linear algebra result\, a family of two or more com
 muting symmetric matrices has a common eigenvector basis and can thus be j
 ointly diagonalized. Such joint eigenvalue problems come in several flavor
 s and they play an important role in a variety of applications\, including
  independent component analysis in signal processing\, multivariate polyno
 mial systems\, tensor decompositions\, and computational quantum chemistry
 .  Perhaps surprisingly\, the development\nof robust numerical algorithms 
 for solving such problems is by no means trivial. To start with\, roundoff
  error or other forms of error will inevitably destroy commutativity assum
 ptions. In turn\, one can at best hope to find approximate solutions to jo
 int eigenvalue problems and\, in\nturn\, most existing approaches are base
 d on optimization techniques\, which may or may not recover the approximat
 e 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
  theoretical explanation for their success by establishing probabilistic g
 uarantees for robust recovery. Through numerical experiments on synthetic 
 and real-world data\, we show that our algorithms reach or outperform stat
 e-of-the-art optimization-based methods. This talk is based on joint work 
 with Haoze He.
LOCATION:Centre for Mathematical Sciences\, MR14
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