Paper Info
Title
The Schur Algorithm Applied to the One-Dimensional Continuous Inverse Scattering Problem
Abstract
The one-dimensional continuous inverse scattering problem can be solved by the Schur algorithm in the discrete-time domain using sampled scattering data. The sampling rate of the scattering data should be increased to reduce the discretization error, but the complexity of the Schur algorithm is proportional to the square of the sampling rate. To improve this tradeoff between the complexity and the accuracy, we propose a Schur algorithm with the Richardson extrapolation (SARE). The asymptotic expansion of the Schur algorithm, necessary for the Richardson extrapolation, is derived in powers of the discretization step, which shows that the accuracy order (with respect to the discretization step) of the Schur algorithm is 1. The accuracy order of the SARE with the N-step Richardson extrapolation is increased to N+1 with comparable complexity to the Schur algorithm. Therefore, the discretization error of the Schur algorithm can be decreased in a computationally efficient manner by the SARE.
Year
DOI
Venue
2013
10.1109/TSP.2013.2259487
IEEE Transactions on Signal Processing
Keywords
Field
DocType
sare,discretization error reduction,sampling rate,schur algorithm,inverse problems,discrete-time domain,extrapolation,reflection coefficient,one-dimensional continuous inverse problem,sampled scattering data,richardson extrapolation,electromagnetic wave scattering,inverse scattering,schur algorithm with the richardson extrapolation
Discretization,Mathematical optimization,Richardson extrapolation,Mathematical analysis,Asymptotic expansion,Extrapolation,Inverse problem,Schur decomposition,Schur complement method,Mathematics,Inverse scattering problem
Journal
Volume
Issue
ISSN
61
13
1053-587X
Citations 
PageRank 
References 
1
0.35
16
Authors
4
Name
Order
Citations
PageRank
Youngchol Choi1532.61
Joohwan Chun239635.12
Tae-Joon Kim358142.12
Jinho Bae432.10