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**Harvard**

Klibanov, M., Bakushinsky, A. och Beilina, L. (2011) *Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess*.

** BibTeX **

@article{

Klibanov2011,

author={Klibanov, M. V. and Bakushinsky, A. B. and Beilina, Larisa},

title={Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess},

journal={Journal of Inverse and Ill - Posed Problems},

issn={0928-0219},

volume={19},

issue={1},

pages={83-105},

abstract={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.},

year={2011},

keywords={Uniqueness theorem, Tikhonov functional, a single value of the level of, error, coefficient inverse problem },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 140758

A1 Klibanov, M. V.

A1 Bakushinsky, A. B.

A1 Beilina, Larisa

T1 Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess

YR 2011

JF Journal of Inverse and Ill - Posed Problems

SN 0928-0219

VO 19

IS 1

SP 83

AB 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.

LA eng

DO 10.1515/jiip.2011.024

LK http://dx.doi.org/10.1515/jiip.2011.024

OL 30