An effective criterion for a stable factorisation of a strictly nonsingular 2 × 2 matrix functions. Utilisation of the ExactMPF package

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• Gennady Mishuris (Aberystwyth University)
• Friday 05 July 2024, 14:30-15:00
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

In this talk, we exploit the functionality of the ExactMPF package to address the general factorization problem of determining whether a given strictly nonsingular 2 × 2 matrix function admits canonical or stable factorization. The idea is to approximate the latter by a sequence of polynomial matrix functions that admit exact factorization while preserving the same properties as the original matrix function. To achieve this goal, we propose an effective sufficient criterion that guarantees that, starting from some element, the given matrix function belongs to a small neighborhood of the stability domain of each subsequent element of the sequence. The theoretical results supporting the method rely on an appropriate normalization of the approximate matrix functions. Additionally, we present some numerical results highlighting the proposed procedure. (Co-Authors: N. Adukova, V. Adukov)

This talk is part of the Isaac Newton Institute Seminar Series series.

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