This paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption ...

A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear
algebraic systems is studied in this paper. An a priori and a posteriori stopping rules
are justified. An algorithm for computing the ...

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear
equations F(u) = f with monotone operators F in a Hilbert space is studied in this paper under less restrictive assumptions on the nonlinear ...

A review of the authors’ results is given. Several methods are discussed for solving nonlinear equations F(u) = f, where F is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A ...

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type ...

An evolution equation, arising in the study of the Dynamical Systems Method (DSM)for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized ...

A nonlinear differential inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear ...