BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Comments on the approximate factorisation of matri
x functions with unstable sets of partial indices
- Gennady Mishuris (Aberystwyth University)
DTSTART;TZID=Europe/London:20190816T153000
DTEND;TZID=Europe/London:20190816T160000
UID:TALK128716AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128716
DESCRIPTION:It is well known for more than 60 years that the s
et of partial indices of a non-singular matrix fun
ction may be unstable under small perturbations of
the matrix [1]. This happens when the difference
between the largest and the smallest indices is la
rger than unity. Although the total index of the m
atrix preserves its value\, this former makes it e
xtremely difficult to use this very powerful metho
d for solving practical problems in this particula
r case. Moreover\, since there does not exist a ge
neral constructive technique for matrix factorisat
ion or even for the determination of the partial i
ndices of the matrix\, this fact looks like an una
voidable obstacle. Following [2]\, in this talk\,
we try to answer a less ambitious question focusin
g on the determination of the conditions allowing
one to construct a family of matrix functions pres
erving a majority of the properties of the origina
l matrix with non-stable partial indices that is c
lose to the original matrix function.

This
work was partially supported by a grant from the S
imons Foundation. GM is also acknowledge Royal Soc
iety for the Wolfson Research Merit Award.

[1] Gohberg I. & Krein M. 1958 Uspekhi Mat. Nau
k.XIII\, 3&ndash\;72 (in Russian).

[2] Mishuris
G\, Rogosin S. 2018 Regular approximate factoriza
tion of a class of matrix-function with an unstabl
e set of partial indices. Proc.R.Soc.A 474:2017027
9. http://dx.doi.org/10.1098/rspa.2017.0279
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR