An Iterative Wiener--Hopf method for triangular matrix functions with exponential factors
Authors
Kisil, Anastasia
Journal Title
SIAM Journal on Applied Mathematics
ISSN
0036-1399
Publisher
Society for Industrial and Applied Mathematics
Volume
78
Issue
1
Pages
45-62
Language
eng
Type
Article
This Version
VoR
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Kisil, A. (2018). An Iterative Wiener--Hopf method for triangular matrix functions with exponential factors. SIAM Journal on Applied Mathematics, 78 (1), 45-62. https://doi.org/10.1137/17M1136304
Abstract
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, at the moment, cannot be obtained. The proposed method could be considered as a generalisation 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 su cient number of iterations could be made arbitrary 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. 1.
Keywords
Wiener--Hopf equations, Riemann-Hilbert problem, iterative methods
Sponsorship
I acknowledge support from the Sultan Qaboos Research Fellowship at Corpus Christi College at University of Cambridge.
Embargo Lift Date
2100-01-01
Identifiers
External DOI: https://doi.org/10.1137/17M1136304
This record's URL: https://www.repository.cam.ac.uk/handle/1810/271693
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