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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:TALK128470AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128470
DESCRIPTION:By an explicit solution of the factorization probl
em we mean the solution that can be found by finit
e number of some steps which we call "explicit".
When we solve a specific factorization problem we
must rigorously define these steps. In this talk w
e will do this for matrix polynomials\, rational m
atrix functions\, analytic matrix functions\, mero
morphic matrix functions\, triangular matrix funct
ions and others. For these classes we describe the
data and procedures that are necessary for the ex
plicit solution of the factorization problem. Sinc
e the factorization problem is unstable\, the expl
icit solvability of the problem does not mean that
we can get its numerical solution. This is the pr
incipal obstacle to use the Wiener-Hopf techniques
in applied problems. For the above mentioned clas
ses the main reason of the instability is the inst
ability of the rank of a matrix. Numerical experi
ments show that the use of SVD for computation of
the ranks often allows us to correctly find the pa
rtial indices for matrix polynomials. To create a
test case set for numerical experiments we have t
o solve the problem exactly. By the exact solution
s of the factorization problem we mean those solut
ions that can be found by symbolic computation. In
the talk we obtain necessary and sufficient condi
tions for the existence of the exact solution to t
he problem for matrix polynomials and propose an a
lgorithm for constructing of the exact solution. T
he solver modules in SymPy and in Maple that imple
ment this algorithm are designed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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