Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle

摘要: We consider the general iteratively regularized Gauss-Newton methods xk+1 = x0 − gαk (F (xk)F (xk))F (xk) ( F (xk)− y (xk)(xk x0) ) for solving nonlinear inverse problems (x) using only available noise yδ of satisfying ‖yδ y‖ ≤ δ with a given small level > 0. In order to produce reasonable approximation sought solution, we terminate iteration by discrepancy principle. Under much weaker conditions derive some further convergence results which improve existing ones and thus expand applied range.