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

Iteratively regularized Gauss–Newton type methods for approximating quasi–solutions of irregular nonlinear operator equations in Hilbert space with an application to COVID–19 epidemic dynamics

“…Also choose connecting mappings and . We approximate the operator by a mapping and consider for (1.1) the approximating equation Various schemes for constructing numerically implementable iterative methods are applicable to the discretized equation (1.8) [2] , [4] , [5] , [6] , [7] . Particularly the method (1.4) can be applied to (1.8) for evaluating approximations of , e.g., [4] , [5] .…”

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

“…Based on a nonlinear diffusion equation as the forward problem, one can formulate the inverse problem of determining the unknown parameter from indirect measured data as a nonlinear operator equation. The iteration methods, such as Landweber [16,17], Levenberg-Marquardt [18,19], and Gauss-Newton [20,21], are a natural manner to solve such equations. However, iteration methods were hindered by issues such as initial guess, complexity, and convergence.…”