University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On explicit and exact solutions of the Wiener-Hopf factorization problem for some matrix functions

On explicit and exact solutions of the Wiener-Hopf factorization problem for some matrix functions

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact INI IT.

WHTW01 - Factorisation of matrix functions: New techniques and applications

By an explicit solution of the factorization problem we
mean the solution that can be found by finite number of some steps which we
call “explicit”.

When we solve a specific factorization problem we must
rigorously define these steps. In this talk we will do this for matrix
polynomials, rational matrix functions, analytic matrix functions, meromorphic
matrix functions, triangular matrix functions and others. For these classes 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 classes the main reason of the
instability 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 the
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.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity