Attractors of iterative processors in the presence of noises (Q1975093)

The author considers the problem of searching for attractors in iterative processes, that is the most important part of the analysis of such processes. Traditional analysis (in the absence of noises) are characterized by the separation of single-point attractors of iterative processes. In the general case, indefinitely nondecreasing noises can substantially distort an attractor. Usually, one deals with the choice of the narrowest possible attractor (and its contracting domain) that contains the attracting point of the original unperturbed process. Expressions for attractors of Newton's method are obtained.