TY - JOUR

T1 - On explicit Wiener-Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix

AU - Ephremidze, L.

AU - Spitkovsky, I.

N1 - Funding Information:
Data accessibility. This article has no additional data. Authors’ contributions. Both authors equally contributed to the design of the proposed algorithms. The first author conducted the numerical experiments and drafted the paper; the second author played the main role in interpreting the data and revising the paper. Both authors approve the final version and agree to be accountable for all aspects of the work. Competing interests. We declare we have no competing interests. Funding. This work was supported by EPSRC grant no EP/R014604/1. L.E. was supported by the Shota Rustaveli National Science Foundation of Georgia (project no. FR-18-2499) and I.S. was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi. Acknowledgements. The authors also thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme ‘Bringing pure and applied analysis together via the Wiener– Hopf technique, its generalizations and applications’ where some work on this paper was undertaken.
Publisher Copyright:
© 2020 The Author(s).

PY - 2020

Y1 - 2020

N2 - As it is known, the existence of the Wiener-Hopf factorization for a given matrix is a well-studied problem. Severe difficulties arise, however, when one needs to compute the factors approximately and obtain the partial indices. This problem is very important in various engineering applications and, therefore, remains to be subject of intensive investigations. In the present paper, we approximate a given matrix function and then explicitly factorize the approximation regardless of whether it has stable partial indices. For this reason, a technique developed in the Janashia-Lagvilava matrix spectral factorization method is applied. Numerical simulations illustrate our ideas in simple situations that demonstrate the potential of the method.

AB - As it is known, the existence of the Wiener-Hopf factorization for a given matrix is a well-studied problem. Severe difficulties arise, however, when one needs to compute the factors approximately and obtain the partial indices. This problem is very important in various engineering applications and, therefore, remains to be subject of intensive investigations. In the present paper, we approximate a given matrix function and then explicitly factorize the approximation regardless of whether it has stable partial indices. For this reason, a technique developed in the Janashia-Lagvilava matrix spectral factorization method is applied. Numerical simulations illustrate our ideas in simple situations that demonstrate the potential of the method.

KW - Janashia-Lagvilava method

KW - Wiener-Hopf factorization

KW - matrix spectral factorization

KW - partial indices

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U2 - 10.1098/rspa.2020.0027rspa20200027

DO - 10.1098/rspa.2020.0027rspa20200027

M3 - Article

AN - SCOPUS:85092336831

VL - 476

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2238

M1 - 20200027

ER -