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Regularization methods for the stable solution of inverse problems. (English) Zbl 0776.65043
The author analyzes some mathematical features, especially concerning the inherent instability (“ill-posedness”) of inverse problems and mathematical techniques (“regularization methods”) for overcoming this essential difficulty in numerical computations. These problems are, usually, “ill-posed”, i.e., their solution is not unique and/or unstable with respect to data perturbations. Many examples from (also, but not exclusively, industrial) applications are given.
Reviewer: G.Dimitriu (Iaşi)

65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65R30 Numerical methods for ill-posed problems for integral equations
65R20 Numerical methods for integral equations
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R30 Inverse problems for PDEs