Journal article, 2011

Suppose that a uniqueness theorem is valid for an ill-posed problem. It is shown then that the distance between the exact solution and terms of a minimizing sequence of the Tikhonov functional is less than the distance between the exact solution and the first guess. Unlike the classical case when the regularization parameter tends to zero, only a single value of this parameter is used. Indeed, the latter is always the case in computations. Next, this result is applied to a specific coefficient inverse problem. A uniqueness theorem for this problem is based on the method of Carleman estimates. In particular, the importance of obtaining an accurate first approximation for the correct solution follows from Theorems 7 and 8. The latter points towards the importance of the development of globally convergent numerical methods as opposed to conventional locally convergent ones. A numerical example is presented.

a single value of the level of

coefficient inverse problem

Uniqueness theorem

error

Tikhonov functional

The University of North Carolina at Charlotte

Russian Academy of Sciences

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

0928-0219 (ISSN) 1569-3945 (eISSN)

Vol. 19 1 83-105Computational Mathematics

10.1515/jiip.2011.024