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 END:VEVENT END:VCALENDAR