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

M. V. Klibanov ; A. B. Bakushinsky ; Larisa Beilina (Institutionen för matematiska vetenskaper, matematik)
Journal of Inverse and Ill - Posed Problems (0928-0219). Vol. 19 (2011), 1, p. 83-105.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Uniqueness theorem, Tikhonov functional, a single value of the level of, error, coefficient inverse problem



Denna post skapades 2011-05-17. Senast ändrad 2016-07-14.
CPL Pubid: 140758

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Tillämpad matematik

Chalmers infrastruktur