Following a recent paper by Mandache (2001 Inverse Problems 17 1435–44),we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to an elliptic inverse problem concerning the determination of inclusions in a conductor by different kinds of boundary measurements and to inverse obstacle acoustic scattering problems andwe show that these problems are exponentially ill-posed.
Examples of exponential instability for inverse inclusion and scattering problems / M. DI CRISTO, L. Rondi. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 19:3(2003), pp. 685-701. [10.1088/0266-5611/19/3/313]
Examples of exponential instability for inverse inclusion and scattering problems
M. DI CRISTO;L. Rondi
2003
Abstract
Following a recent paper by Mandache (2001 Inverse Problems 17 1435–44),we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to an elliptic inverse problem concerning the determination of inclusions in a conductor by different kinds of boundary measurements and to inverse obstacle acoustic scattering problems andwe show that these problems are exponentially ill-posed.
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