Iterative Newton Type Algorithms and Its Applications to Inverse Gravimetry Problem

Abstract

The paper gives a brief overview of approaches to the construction of iterative processes
of the Newton and gradient type for stable approximation of solutions to nonlinear
irregular operator equations in Hilbert spaces. For two-stage algorithms based on Lavrentiev
regularization scheme and a modified Newton’s method the convergence theorem are
formulated and the results of numerical solution to three-dimensional inverse gravimerty
problem for two-layer model are discussed.