An iterative scheme for solving nonlinear equations with monotone operators
For researchers in inverse problems and nonlinear operator equations, this provides a new algorithmic framework with theoretical guarantees, though it is an incremental extension of existing DSM methods.
The paper introduces a Dynamical Systems Method (DSM) algorithm for stably solving ill-posed nonlinear equations with monotone operators, proving convergence and proposing a new discrepancy principle with stopping rules.
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A new discrepancy principle is proposed and justified. A priori and a posteriori stopping rules for the DSM algorithm are formulated and justified.