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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:TALK128470@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:By an explicit solution of the factorization problem we mean t
 he solution that can be found by finite number of some steps which we call
  "explicit".  When we solve a specific factorization problem we must rigor
 ously define these steps. In this talk we will do this for matrix polynomi
 als\, rational matrix functions\, analytic matrix functions\, meromorphic 
 matrix functions\, triangular matrix functions and others. For these class
 es we describe the data and procedures that are necessary for the explicit
  solution of the factorization problem. Since the factorization problem is
  unstable\, the explicit solvability of the problem does not mean that we 
 can get its numerical solution. This is the principal obstacle to use the 
 Wiener-Hopf techniques in applied problems. For the above mentioned classe
 s the main reason of the instability is the instability of the rank of a m
 atrix.  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 existe
 nce of the exact solution to the problem for matrix polynomials and propos
 e 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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