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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(δ 1/2 ) for the regularized solution where δ is the noise level of the data (y δ -y 0 δ). The paper is illustrated by several examples including parameter estimation problems in one-dimensional case.
Reviewer: G.Vainikko

MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)