Regularization Algorithms for Ill-Posed Problems

Convexification Method for an Inverse Scattering Problem and Its Performance for Experimental Backscatter Data for Buried Targets

“…We now follow the classical Tikhonov regularization concept [4,40]. By this concept, we should assume that there exists an exact solution V * (x) of the problem (5.7)-(5.8) with the noiseless data ψ 0 * (x), ψ 1 * (x).…”

“…We now need to estimate the convergence rate of this sequence to the exact solution. To do this, we follow the Tikhonov regularization concept [4,40] in Theorem 7.6 via assuming that the exact solution p * ∈ B(R).…”

Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems

“…Thus, the induction is complete. We prove Equation (14) by induction in the same manner as Equation (13).…”

“…The convergence rate analysis under the logarithmic source condition in Equation (7) has been successfully studied by Hohage [5] for the iteratively regularized Gauss-Newton method and by Deuflhard et al [13] for Landweber's iteration. Current studies of source condition may be found, e.g., in Romanov et al [11], Bakushinsky et al [14], Schuster et al [15] and Albani et al [16].…”

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

“…In this paper, the object of our interest are iteratively regularized Gauss–Newton type methods for equation (1.1). The following class of such methods is studied in detail, see [1] , [2] and references therein: For generalizations to the Banach space case we refer to [3] . Here and are initial guesses for , and is a sequence of regularization parameters satisfying …”