Regularization methods for the stable solution of inverse problems. (English) Zbl 0776.65043

Engl, Heinz W.

Surv. Math. Ind. 3, No. 2, 71-143 (1993).

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)

MSC:

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

Keywords:

inverse problems; ill-posed problems; regularization; parameter identification; nondestructive testing; Steel casting