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Inverse free iterative methods for nonlinear ill-posed operator equations. (English) Zbl 1309.47065
Summary: We present a new iterative method which does not involve inversion of the operators for obtaining an approximate solution for the nonlinear ill-posed operator equation $$F(x)=y$$. The proposed method is a modified form of Tikhonov gradient (TIGRA) method considered by R. Ramlau [Inverse Probl. 19, No. 2, 433–465 (2003; Zbl 1029.65059)]. The regularization parameter is chosen according to the balancing principle considered by S. Pereverzev and E. Schock [SIAM J. Numer. Anal. 43, No. 5, 2060–2076 (2005; Zbl 1103.65058)]. The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.

##### MSC:
 47J06 Nonlinear ill-posed problems 65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
TIGRA
Full Text:
##### References:
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