Prosiectau fesul blwyddyn
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We discuss an explicit algorithm for solving the Wiener-Hopf 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 Wiener-Hopf 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 |
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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 ar-lein cynnar | 06 Gorff 2022 |
Dynodwyr Gwrthrych Digidol (DOIs) | |
Statws | Cyhoeddwyd - 27 Gorff 2022 |
Ôl bys
Gweld gwybodaeth am bynciau ymchwil 'An explicit Wiener-Hopf factorization algorithm for matrix polynomials and its exact realizations within ExactMPF package'. Gyda’i gilydd, maen nhw’n ffurfio ôl bys unigryw.Setiau Data
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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
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EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications
Mishuris, G. (Prif Ymchwilydd)
Horizon 2020 -European Commission
01 Medi 2021 → 31 Awst 2025
Prosiect: Ymchwil a ariannwyd yn allanol
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Wolfson Visiting Fellowship - Professor Victor Eremeyev
Mishuris, G. (Prif Ymchwilydd)
01 Gorff 2021 → 30 Meh 2023
Prosiect: Ymchwil a ariannwyd yn allanol