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SUMMARY:The Janashia–Lagvilava Method of Matrix Spectral Factorization: 
 Recent Advances and Exponential Acceleration
DTSTART:20260626T131500Z
DTEND:20260626T141500Z
DTSTAMP:20260702T051600Z
UID:indico-event-1419@math-events.uni-bonn.de
DESCRIPTION:Speakers: Lasha Ephremidze (Kutaisi International University a
 nd Razmadze Mathematical Institute)\n\nAbstract:\nMatrix spectral factoriz
 ation is a classical problem with numerous applications in prediction theo
 ry\, control engineering\, signal processing\, communications\, and mathem
 atical physics. While several computational approaches have been developed
  over the past decades\, reliable factorization of large-scale or nearly s
 ingular matrix functions remains a challenging task.\nIn this talk\, I wil
 l present the Janashia–Lagvilava method of matrix spectral factorization
 \, originally developed at the A. Razmadze Mathematical Institute. The met
 hod is based on a recursive reduction of the matrix factorization problem 
 to a sequence of scalar spectral factorizations and has been shown to poss
 ess strong numerical stability properties\, particularly in situations whe
 re traditional algorithms encounter difficulties.\nAfter reviewing the mai
 n ideas behind the method and its theoretical foundations\, I will discuss
  several recent developments\, including a new non-commutative reformulati
 on of the algorithm\, which leads to an exponential acceleration of the co
 mputational procedure. Numerical experiments demonstrate dramatic performa
 nce improvements for large-scale matrix functions while preserving the rob
 ustness and accuracy of the original method.\nThe results illustrate how c
 lassical ideas from harmonic analysis can be combined with modern computat
 ional techniques to address contemporary challenges in large-scale data an
 alysis. \n \n\nhttps://math-events.uni-bonn.de/event/1419/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1419/
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