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A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
Applications of Mathematics, Tome 38 (1993) no. 6, pp. 479-487

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MR Zbl
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
DOI : 10.21136/AM.1993.104570
Classification : 35R30, 47H15, 47J25, 65F15, 65J15, 65J20, 65M30
Keywords: nonlinear inverse problems; parameter choice strategy; nonlinear ill- posed problems; Hilbert spaces; Tikhonov regularization; convergence rate; numerical examples 
Scherzer, Otmar. A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates. Applications of Mathematics, Tome 38 (1993) no. 6, pp. 479-487. doi: 10.21136/AM.1993.104570
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104570/}
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