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The Schur algorithm and its applications. (English) Zbl 0577.65112

The paper attempts to demonstrate the widespread applicability of the fast Cholesky and Schur recursions for the study of inverse scattering problems. The algorithms are derived by using a layer stripping principle to reconstruct a scattering medium, described by symmetric two-component wave equations, for the case when the medium is probed by impulsive waves. The applicability of these algorithms to the reconstruction of a nonuniform lossless transmission line, and to the inverse problem for a one-dimensional layered acoustic medium is demonstrated. Further, it is shown that the linear least-squares estimation problem for a stationary process could be posed as an inverse scattering problem, and solved by the Schur algorithm.
Reviewer: N.D.Sengupta

MSC:

65Z05 Applications to the sciences
60G35 Signal detection and filtering (aspects of stochastic processes)
93E10 Estimation and detection in stochastic control theory
86A15 Seismology (including tsunami modeling), earthquakes
86A20 Potentials, prospecting
78A45 Diffraction, scattering
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
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