The philosophy of the approximate global convergence for multidimensional coefficient inverse problems
Journal article, 2012
Both the most important and the most challenging question in the numerical
treatment of a Multidimensional Coefficient Inverse Problem for a PDE is the
following: How to obtain a point in a small neighborhood of the exact
solution without any a priori knowledge of this solution? The recent
numerical experience of the authors for two types of Multidimensional
Coefficient Inverse Problems shows that in order to develop a truly
efficient algorithm addressing this question, it is necessary to make some
reasonable approximations which cannot be rigorously justified.
Nevertheless, numerical studies show that corresponding algorithms work
quite well. The authors call this approach "approximate
global convergence/reconstruction". The goal of the paper is to present a
short illustrative review of this philosophy.
approximate global convergence
coefficient inverse problems