Finite dimensional iteratively regularized Gauss–Newton type methods and application to an inverse problem of the wave tomography with incomplete data range

Abstract

ABSTRACTFor an approximate solution of irregular nonlinear operator equations with a smooth operator in Hilbert space, a class of numerically implementable iteratively regularized Gauss–Newton type methods is constructed and studied. The methods include a general finite dimensional approximation for equations under consideration and cover the projection, collocation, and quadrature discretization schemes. Using an a priori 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. An iteratively regularized quadrature process is applied to an inverse problem of the wave tomography in a model with the incomplete data range.