Diffraction problems and inversion of infinite structured matrices
type: Item
instance of: scholarly article
title: Diffraction problems and inversion of infinite structured matrices
zbMATH Open document ID: 0957.65020
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-08-27T00:00:00Z
review text: Diffraction problems generated by the Helmholtz equation are considered that can be reduced to solving infinite systems of linear equations \(SX= F\), where the operators \(S\) satisfy an identity of the form \(AS-SB= P_1P^*_1\) where \(A\) and \(B\) are diagonal matrices and \(P_1\) and \(P_2\) have a finite number of columns. An efficient solution method is presented and applied to the case of diffraction in the planar waveguide with a cross-sectional jump, absolutely soft upper boundary, and absolutely hard lower boundary.
reviewed by: F. Szidarovszky
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A50
Mathematics Subject Classification ID: 78M20
zbMATH DE Number: 1497253
zbMATH Keywords: diffraction
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: infinite systems of linear equations
zbMATH Keywords: waveguide
author: Alexander L. Sakhnovich
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6837
OpenAlex ID: W1993108245
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DOI: 10.1006/JMAA.2000.6837
description: scientific article; zbMATH DE number 1497253