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SUMMARY:Comments on the approximate factorisation of matrix functions with
  unstable sets of partial indices - Gennady Mishuris (Aberystwyth Universi
 ty)
DTSTART:20190816T143000Z
DTEND:20190816T150000Z
UID:TALK128713@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:It is well known for more than 60 years that the set of partia
 l indices of a non-singular matrix function may be unstable under small pe
 rturbations of the matrix [1]. This happens when the difference between th
 e largest and the smallest indices is larger than unity. Although the tota
 l index of the matrix preserves its value\, this former makes it extremely
  difficult to use this very powerful method for solving practical problems
  in this particular case. Moreover\, since there does not exist a general 
 constructive technique for matrix factorisation or even for the determinat
 ion of the partial indices of the matrix\, this fact looks like an unavoid
 able obstacle. Following [2]\, in this talk\, we try to answer a less ambi
 tious question focusing on the determination of the conditions allowing on
 e to construct a family of matrix functions preserving a majority of the p
 roperties of the original matrix with non-stable partial indices that is c
 lose to the original matrix function.<br> <br> This work was partially sup
 ported by a grant from the Simons Foundation. GM is also acknowledge Royal
  Society for the Wolfson Research Merit Award. <br> <br> [1] Gohberg  I. &
 amp\;  Krein M. 1958 Uspekhi Mat. Nauk.XIII\, 3&ndash\;72 (in Russian).<br
 > [2] Mishuris G\, Rogosin S. 2018 Regular approximate factorization of a 
 class of matrix-function with an unstable set of partial indices. Proc.R.S
 oc.A 474:20170279. http://dx.doi.org/10.1098/rspa.2017.0279<br>
LOCATION:Seminar Room 1\, Newton Institute
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