ITERATIVE METHODS FOR APPROXIMATE SOLUTION OF INVERSE PROBLEMS

By T. JAERN

CONTENTS 1 IRREGULAR EQUATIONS AS ILL–POSED PROBLEMS PRELIMINARIES IRREGULAR EQUATIONS AND CONTEMPORARY THEORY OF ILL–POSED PROBLEMS 2 REGULARIZATION METHODS FOR LINEAR EQUATIONS GENERALSCHEMEOFCONSTRUCTINGAF?NEREGULARIZATIONALGORITHMS FOR LINEAR EQUATIONS IN HILBERT SPACE GENERAL SCHEME OF CONSTRUCTING REGULARIZATION ALGORITHMS IN BANACH SPACE NECESSITYOFSOURCEWISEREPRESENTATIONFORRATEOFCONVERGENCE ESTIMATES IN BANACH SPACE 3 PARAMETRIC APPROXIMATIONS OF SOLUTIONS TO NONLINEAR OPERATOR EQUATIONS CLASSICAL LINEARIZATION SCHEMES PARAMETRIC APPROXIMATIONS OF IRREGULAR EQUATIONS PARAMETRIC APPROXIMATIONS IN INVERSE SCATTERING PROBLEM 4 ITERATIVE PROCESSES ON THE BASIS OF PARAMETRIC APPROXIMATIONS GENERALIZEDGAUSS–NEWTONTYPEMETHODSFORNONLINEARIRREGULAR EQUATIONS IN HILBERT SPACE NECESSITYOFSOURCEWISEREPRESENTATIONFORRATEOFCONVERGENCE ESTIMATES OF GAUSS–NEWTON TYPE METHODS GENERALIZEDNEWTON–KANTOROVICHTYPEMETHODSFORNONLINEAR IRREGULAR EQUATIONS IN BANACH SPACE NECESSITYOFSOURCEWISEREPRESENTATIONFORRATEOFCONVERGENCE ESTIMATES OF NEWTON–KANTOROVICH TYPE METHODS CONTINUOUSMETHODSFORIRREGULAROPERATOREQUATIONSINHILBERT AND BANACH SPACES 5 STABLE ITERATIVE PROCESSES STABLE GRADIENT PROJECTION METHODS WITH ADAPTIVE CHOICE OF PROJECTORS PROJECTION METHOD WITH A PRIORI CHOICE OF PROJECTORS PROJECTION METHOD FOR FINDING QUASISOLUTIONS STABLE METHODS ON THE BASIS OF PARAMETRIC APPROXIMATIONS STABLECONTINUOUSAPPROXIMATIONSANDATTRACTORSOFDYNAMICAL SYSTEMS IN HILBERT SPACE ITERATIVELY REGULARIZED GRADIENT METHOD AND ITS CONTINUOUS VERSION ONCONSTRUCTIONOFSTABLEITERATIVEMETHODSFORSMOOTHIRREGULAR EQUATIONS AND EQUATIONS WITH DISCONTINUOUS OPERATORS 6 APPLICATIONS OF ITERATIVE METHODS RECONSTRUCTION OF BOUNDED HOMOGENEOUS INCLUSION RECONSTRUCTION OF SEPARATING SURFACE OF HOMOGENEOUS MEDIA BY MEASUREMENTS OF GRAVITATIONAL ATTRACTION FORCE ACOUSTIC INVERSE MEDIUM PROBLEM INVERSE ACOUSTIC OBSTACLE SCATTERING FAR FIELD OBSERVATION INVERSE ACOUSTIC OBSTACLE SCATTERING NEAR FIELD OBSERVATION 7 NOTES REFERENCES