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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The ExactMPF: the exact matrix polynomial factoris
 ation - Natalia Adukova (Aberystwyth University)
DTSTART;TZID=Europe/London:20240705T140000
DTEND;TZID=Europe/London:20240705T143000
UID:TALK215023AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/215023
DESCRIPTION:\nIn this talk\, we discuss a notion of exact solu
 tion of the Wiener&ndash\;Hopf factorisation probl
 em for matrix polynomials. By the exact solution\,
  we understand the fulfilment of the following two
  conditions: 1) the input data belongs to the Gaus
 sian field Q(i) of complex rational numbers and 2)
  all (finite) steps of the explicit algorithm can 
 be performed in the rational arithmetic. Since the
  factorisation is generally speaking unstable with
  respect to small perturbation\, those requirement
 s are crucial to guarantee that the instability is
 sue does not arise. Unfortunately\, even the condi
 tions 1) &ndash\; 2) are not sufficient for the ex
 act solution to exist. We have proven the followin
 g necessary and sufficient condition: a matrix pol
 ynomial over the field of Gaussian rational number
 s admits the exact Wiener&ndash\;Hopf factorisatio
 n if and only if its determinant is exactly factor
 able. For the factorisation\, we use the explicit 
 algorithm based on the method of essential polynom
 ials. It has been proven already its efficiency (i
 t provides both left and right factorisation simul
 taneously) but is rather technical. To help possib
 le users\, we develop its realisation within an Ex
 actMPF package in Maple Software. We illustrate it
 s performance presenting several examples. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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