The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations

M. I. Belishev; V. Yu. Gotlib; S. A. Ivanov

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 2, page 307-327
  • ISSN: 1292-8119

Abstract

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This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of this complication. A theoretical introduction to the BC-method is included.

How to cite

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Belishev, M. I., Gotlib, V. Yu., and Ivanov, S. A.. "The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations." ESAIM: Control, Optimisation and Calculus of Variations 2 (2010): 307-327. <http://eudml.org/doc/197346>.

@article{Belishev2010,
abstract = { This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of this complication. A theoretical introduction to the BC-method is included. },
author = {Belishev, M. I., Gotlib, V. Yu., Ivanov, S. A.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Multidimensional inverse problem / Spectral data; Recovering of a density / Boundary control theory / BC-method / Geometrical optics / Numerical testing .; boundary control method; multidimensional spectral inverse problem; algorithm},
language = {eng},
month = {3},
pages = {307-327},
publisher = {EDP Sciences},
title = {The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations},
url = {http://eudml.org/doc/197346},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Belishev, M. I.
AU - Gotlib, V. Yu.
AU - Ivanov, S. A.
TI - The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 2
SP - 307
EP - 327
AB - This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of this complication. A theoretical introduction to the BC-method is included.
LA - eng
KW - Multidimensional inverse problem / Spectral data; Recovering of a density / Boundary control theory / BC-method / Geometrical optics / Numerical testing .; boundary control method; multidimensional spectral inverse problem; algorithm
UR - http://eudml.org/doc/197346
ER -

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