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We discuss an explicit algorithm for solving the WienerHopf factorization problem for matrix polynomials. By an exact solution of the problem, we understand the one constructed by a symbolic computation. Since the problem is, generally speaking, unstable, this requirement is crucial to guarantee that the result following from the explicit algorithm is indeed a solution of the original factorization problem. We prove that a matrix polynomial over the field of Gaussian rational numbers admits the exact WienerHopf factorization if and only if its determinant is exactly factorable. Under such a condition, we adapt the explicit algorithm to the exact calculations and develop the ExactMPF package realized within the Maple Software. The package has been extensively tested. Some examples are presented in the paper, while the listing is provided in the electronic supplementary material. If, however, a matrix polynomial does not admit the exact factorization, we clarify a notion of the numerical (or approximate) factorization that can be constructed by following the explicit factorization algorithm. We highlight possible obstacles on the way and discuss a level of confidence in the final result in the case of an unstable set of partial indices. The full listing of the package ExactMPF is given in the electronic supplementary material.
Iaith wreiddiol  Saesneg 

Rhif yr erthygl  20210941 
Nifer y tudalennau  22 
Cyfnodolyn  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Cyfrol  478 
Rhif cyhoeddi  2263 
Dyddiad arlein cynnar  06 Gorff 2022 
Dynodwyr Gwrthrych Digidol (DOIs)  
Statws  Cyhoeddwyd  27 Gorff 2022 
Ôl bys
Gweld gwybodaeth am bynciau ymchwil 'An explicit WienerHopf factorization algorithm for matrix polynomials and its exact realizations within ExactMPF package'. Gyda’i gilydd, maen nhw’n ffurfio ôl bys unigryw.Setiau Data

Supplementary material from "An explicit Wiener–Hopf factorization algorithm for matrix polynomials and its exact realizations within ExactMPF package"
Adukov, V. M., Adukova, N. V. & Mishuris, G., Royal Society, 23 Meh 2022
Dangosydd eitem ddigidol (DOI): 10.6084/m9.figshare.c.6060394
Set ddata

EffectFact: Effective Factorisation techniques for matrixfunctions: Developing theory, numerical methods and impactful applications
Horizon 2020 European Commission
01 Medi 2021 → 31 Awst 2025
Prosiect: Ymchwil a ariannwyd yn allanol
