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SUMMARY:On explicit and exact solutions of the Wiener-Hopf factorization p
roblem for some matrix functions - Victor Adukov (South Ural State Univers
ity )
DTSTART:20190813T150000Z
DTEND:20190813T153000Z
UID:TALK128473@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:By an explicit solution of the factorization problem we
mea
n the solution that can be found by finite number of some steps which wecall "explicit".
When we solve a specific factorization problem w
e must
rigorously define these steps. In this talk we will do this for
matrix
polynomials\, rational matrix functions\, analytic matrix functi
ons\, meromorphic
matrix functions\, triangular matrix functions and ot
hers. For these classes we
describe the data and procedures that are ne
cessary for the explicit solution
of the factorization problem. Since t
he factorization problem is unstable\, the
explicit solvability of the
problem does not mean that we can get its numerical
solution. This is t
he principal obstacle to use the Wiener-Hopf techniques in
applied prob
lems. For the above mentioned classes the main reason of the
instabilit
y is the instability of the rank of a matrix.
Numerical experiments
show that the use of SVD for
computation of the ranks often allows us
to correctly find the partial indices
for matrix polynomials.
To
create a test case set for numerical experiments we
have to solve the
problem exactly. By the exact solutions of the factorization
problem we
mean those solutions that can be found by symbolic computation. In
the
talk we obtain necessary and sufficient conditions for the existence of t
he
exact solution to the problem for matrix polynomials and propose an
algorithm
for constructing of the exact solution. The solver modules in
SymPy and in
Maple that implement this algorithm are designed.
LOCATION:Seminar Room 1\, Newton Institute
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