Abstract
We construct and study a class of numerically implementable iteratively regularized Gauss–Newton type methods for approximate solution of irregular nonlinear operator equations in Hilbert space. The methods include a general finite-dimensional approximation for equations under consideration and cover the projection, collocation and quadrature discretization schemes. Using an a posteriori stopping rule for the iterative processes and the standard source condition on the solution, we establish accuracy estimates for the approximations generated by the methods. We also investigate projected versions of the processes which take into account a priori information about a convex compact containing the solution. An iteratively regularized quadrature process is applied to an inverse 2D problem of gravimetry.
Dedicated to Professor Mikhail V. Klibanov on the occasion of the 70th anniversary
Funding source: Russian Science Foundation
Award Identifier / Grant number: 20-11-20085
Funding statement: The work was supported by the Russian Science Foundation Grant No. 20–11–20085.
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