On explicit Wiener-Hopf factorization of 2 x 2 matrices in a vicinity of a given matrix
On explicit Wiener-Hopf factorization of 2 x 2 matrices in a vicinity of a given matrix
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DOI：
10.1098/rspa.2020.0027
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发表时间：
2020-06-24
影响因子：
3.5
通讯作者：
Spitkovsky, I.
中科院分区：
文献类型：
--
作者：
Ephremidze, L.;Spitkovsky, I.
众所周知，对于给定矩阵，Wiener-Hopf分解的存在性是一个研究得很好的问题。严重的困难出现，但是，当一个需要计算的因素近似，并获得部分指标。这个问题在各种工程应用中非常重要，因此仍然是深入研究的主题。在本文中，我们近似一个给定的矩阵函数，然后显式分解的近似，无论它是否有稳定的部分指标。出于这个原因，在Janashia-Lagvilava矩阵谱分解方法中开发的技术被应用。数值模拟说明了我们的想法，在简单的情况下，证明了该方法的潜力。
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.