Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess
Artikel i vetenskaplig tidskrift, 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

Författare

M. V. Klibanov

The University of North Carolina at Charlotte

A. B. Bakushinsky

Russian Academy of Sciences

Larisa Beilina

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Journal of Inverse and Ill-Posed Problems

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

Vol. 19 1 83-105

Ämneskategorier

Beräkningsmatematik

DOI

10.1515/jiip.2011.024