ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 10, 15, 17 Hinestroza, Doris, Universidad del Valle Regularization Techniques for Nonlinear Inverse Problems Many inverse problems in practical problem in sciences, technology and medicine can be reduced to solving the equation given by

(F ∘ Ψ)(x) = y,

where Ψ : C ⊆ X → Y and F : Y → Z are nonlinear weakly sequentially operators between the Hilbert Spaces X, Y, Z and C is a bounded subset of X. These operators contain the internal structure of the system and the right hand side is a given data, and x is a desired solution. This problem is ill-posed and difficult to solve. In order to address the ill-podness of this problem we applied a new generalization of Tikhonov Regularization. Results on existence, stability and convergence rates are presented. Some numerical examples illustrating the behavior of the algorithm in practical situations. Reference: G. Chavent and K. Kunish, Regularization in State Space, Mathematical Modelling and Numerical Analysis, Vol. 27, N0.5, 1993, pp. 535-