Report
Normalisation of Wiener--Hopf Factorisation for Matrix Functions
| Τίτλος: | Normalisation of Wiener--Hopf Factorisation for Matrix Functions |
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| Συγγραφείς: | Adukova, Nataliia, Adukov, Victor |
| Έτος έκδοσης: | 2026 |
| Θεματικοί όροι: | Complex Variables, 30E25, 47A68, 15A23 |
| Περιγραφή: | {For a matrix function $A(t)$, we study the normalisation of its Wiener--Hopf factorisation $A(t)=A_-(t)D(t)A_+(t)$ which guarantees the uniqueness of the factors $A_\pm(t)$. Previously, this problem was investigated for second-order matrix functions, the stable factorisation, and the factorisation of matrix functions with distinct partial indices. The main tools for solving the problem of normalisation are the theorem of I.C. Gohberg and M.G. Krein on a general form of the factors $A_\pm$, a Birkhoff factorisation of matrix functions, and a block PLU factorisation of the numerical matrix $A_-(\infty)$. To solve the normalisation problem, a concept of P-normalised factorisation is introduced. The Birkhoff factorisation of matrix functions plays a key role in defining this concept. The permutation matrix $P$ is determined by PLU factorisation of the numerical matrix $A_-(\infty)$. We proved that any invertible matrix function $A(t)$ admits P-normalisation. This normalisation guarantees the uniqueness of the Wiener--Hopf factorisation. The P-normalised factorisation of $A(t)$ allows us to find the Birkhoff factorisation of $A(t)$. Without normalisation, it is impossible to obtain explicit estimates of the absolute errors in the approximate computation of the factorisation factors.} 22 pages, without tables and figures |
| Τύπος εγγράφου: | Working Paper |
| DOI: | 10.48550/arXiv.2610.07957 |
| Σύνδεσμος πρόσβασης: | https://arxiv.org/abs/2610.07957 |
| Αριθμός Καταχώρησης: | edsarx.2610.07957 |
| Βάση Δεδομένων: | arXiv |
| DOI: | 10.48550/arXiv.2610.07957 |
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