Improved Accuracy Estimation of the Tikhonov Method for Ill-Posed Optimization Problems in Hilbert Space - Kokurin, M. M. (Computational mathematics and mathematical physics, 2023)
The Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional. Assuming that the sought solution satisfies the source condition, an accuracy estimate for the Tikhonov method is obtained in terms of the regularization parameter. Previously, such an estimate was obtained only under the assumption that the functional is convex or under a structural condition imposed on its nonlinearity. Additionally, a new accuracy estimate for the Tikhonov method is obtained in the case of an approximately specified functional.