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

Published online by Cambridge University Press:  15 August 2002

M. I. Belishev ,
V. Yu. Gotlib  and
S. A. Ivanov
M. I. Belishev
Affiliation:
[email protected]
V. Yu. Gotlib
Affiliation:
[email protected]
S. A. Ivanov
Affiliation:
[email protected]
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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.

Keywords

Multidimensional inverse problem / Spectral dataRecovering of a density / Boundary control theory / BC-method / Geometrical optics / Numerical testing .
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 2 , 1997 , pp. 307 - 327
Copyright
© EDP Sciences, SMAI, 1997

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