| Consider a nonlinear operator equation Fz=0, F:H→H, where H is a real Hilbert space. In order to avoid the ill-posed inversion of the Frechet derivative operator, certain regularized procedures are suggested. A two-step iterative scheme based on the idea of global linearization is proposed. A convergence theorem is proved. A general approach to the construction of continuously regularized methods is given. Its applications are studied. In particular continuous processes for ill-posed equations with nonmonotone operators are constructed and the convergence analysis is presented. The above algorithms are tested on practically important problems: inverse problem of gravimetry, inverse scattering problem with fixedenergy phase shifts, the problem of numerical differentiation, the precise computation of Feigenbaum's constants. The numerical results are obtained. Some other regularized methods are investigated. |
