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Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. (English) Zbl 0695.65037

The authors study Tikhonov regularization of the nonlinear ill-posed problem \(F(x)=y_ 0\), 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 \(O(\delta^{1/2})\) for the regularized solution where \(\delta\) is the noise level of the data \((\| y_{\delta}-y_ 0\| \leq \delta)\). The paper is illustrated by several examples including parameter estimation problems in one-dimensional case.
Reviewer: G.Vainikko

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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