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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On explicit and exact solutions of the Wiener-Hopf
factorization problem for some matrix functions -
Victor Adukov (South Ural State University )
DTSTART;TZID=Europe/London:20190813T160000
DTEND;TZID=Europe/London:20190813T163000
UID:TALK128473AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128473
DESCRIPTION:By an explicit solution of the factorization probl
em we
mean the solution that can be found by fi
nite number of some steps which we
call "explic
it".
When we solve a specific factorization
problem we must
rigorously define these steps.
In this talk we will do this for matrix
polyno
mials\, rational matrix functions\, analytic matri
x functions\, meromorphic
matrix functions\, tr
iangular matrix functions and others. For these cl
asses we
describe the data and procedures that
are necessary for the explicit solution
of the
factorization problem. Since the factorization pro
blem is unstable\, the
explicit solvability of
the problem does not mean that we can get its nume
rical
solution. This is the principal obstacle
to use the Wiener-Hopf techniques in
applied pr
oblems. For the above mentioned classes the main r
eason of the
instability is the instability of
the rank of a matrix.
Numerical experiments
show that the use of SVD for
computation of th
e ranks often allows us to correctly find the part
ial indices
for matrix polynomials.
To c
reate a test case set for numerical experiments we
have to solve the problem exactly. By the exac
t solutions of the factorization
problem we mea
n those solutions that can be found by symbolic co
mputation. In
the talk we obtain necessary and
sufficient conditions for the existence of the
exact solution to the problem for matrix polynomia
ls and propose an algorithm
for constructing of
the exact solution. The solver modules in SymPy a
nd in
Maple that implement this algorithm are d
esigned.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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