Boundary control in reconstruction of manifolds and metrics (the BC method)

1 October 1997

journal article
review article
Published by IOP Publishing in Inverse Problems

Vol. 13 (5) , R1-R45
https://doi.org/10.1088/0266-5611/13/5/002

Abstract

One of the approaches to inverse problems based upon their relations to boundary control theory (the so-called BC method) is presented. The method gives an efficient way to reconstruct a Riemannian manifold via its response operator (dynamical Dirichlet-to-Neumann map) or spectral data (a spectrum of the Beltrami - Laplace operator and traces of normal derivatives of the eigenfunctions). The approach is applied to the problem of recovering a density, including the case of inverse data given on part of a boundary. The results of the numerical testing are demonstrated.

Keywords

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