An Iterative Wiener-Hopf Method for Triangular Matrix Functions with Exponential Factors
An Iterative Wiener-Hopf Method for Triangular Matrix Functions with Exponential Factors
复制标题
具有指数因子的三角矩阵函数的迭代Wiener-Hopf方法
DOI：
10.1137/17m1136304
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
A. Kisil
中科院分区：
文献类型：
--
作者：
A. Kisil
本文介绍了一类Wiener-Hopf方程的一种新的构造近似解的方法。这是特别有用的，因为这类Wiener-Hopf方程的精确解目前无法获得。所提出的方法可以被认为是“极点去除”技术和史瓦西级数的推广。并证明了收敛性准则。近似中的误差被明确地估计，并且通过足够数量的迭代，它可以任意小。通常，出于实际目的，仅需要几次迭代。数值例子表明，所提出的方法的优点的理论说明。这种方法的动机和成功地应用于声学问题。
This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations currently cannot be obtained. The proposed method could be considered as a generalization of the “pole removal” technique and Schwarzschild's series. The criteria for convergence is proved. The error in the approximation is explicitly estimated, and by a sufficient number of iterations it could be made arbitrarily small. Typically only a few iterations are required for practical purposes. The theory is illustrated by numerical examples that demonstrate the advantages of the proposed procedure. This method was motivated by and successfully applied to problems in acoustics.