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Zbl 0695.65037
Engl, Heinz W.; Kunisch, Karl; Neubauer, Andreas
Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems.
(English)
[J] Inverse Probl. 5, No.4, 523-540 (1989). ISSN 0266-5611

The authors study Tikhonov regularization of the nonlinear ill-posed problem $F(x)=y\sb 0$, where F is a continuous weakly closed operator between Hilbert spaces X and Y. They show that the Tikhonov regularization is a stable method and give conditions to guarantee the convergence rate $O(\delta\sp{1/2})$ for the regularized solution where $\delta$ is the noise level of the data $(\Vert y\sb{\delta}-y\sb 0\Vert \le \delta)$. The paper is illustrated by several examples including parameter estimation problems in one-dimensional case.
[G.Vainikko]
MSC 2000:
*65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: inverse problems; Tikhonov regularization; nonlinear ill-posed problem; Hilbert spaces; convergence rate; parameter estimation

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