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SUMMARY:On approximate Wiener-Hopf factorization of 2 × 2 matrices - Lash
 a Ephremidze (Tbilisi State University)
DTSTART:20240703T094500Z
DTEND:20240703T101500Z
UID:TALK215437@talks.cam.ac.uk
DESCRIPTION:We present a novel algorithm for the factorization of triangul
 ar polynomial 2x2 matrices. Our algorithm offers flexibility in choosing b
 etween 'exact' and 'natural' pairs of partial indices. Integrated into the
  general Winer-Hopf factorization algorithm for 2x2 matrices\, as describe
 d in https://doi.org/10.1098/rspa.2020.0027\, the approach offers a versat
 ile method applicable to practical scenarios. Specifically\, given a matri
 x function S\, our method enables the construction of a Wiener-Hopf factor
 ization for an approximate matrix with manageable factors\, even when the 
 exact factorization of S may involve large factors. These large factors of
  S are presumed to arise due to inaccuracies in the construction process o
 f S\, rendering its exact factorization impractical. The cases where S or 
 its approximation have unstable partial indices are not excluded. Thus\, s
 electing a reasonable factorization of the approximated matrix function S 
 emerges as a natural choice\, facilitating an automatic determination of t
 he partial indices\, which in turn\, could serve as a novel regularization
  procedure.&nbsp\;\n(Co-Authors: G. Mishuris\, I. Spitkovsky)
LOCATION:Seminar Room 1\, Newton Institute
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