  The article deals with gradient-like iterative methods for solving nonlinear
operator equations on Hilbert and Banach spaces. The authors formulate a
general principle of studying such methods. This principle allows to formulate
simple conditions of convergence of the method under consideration, to estimate
the rate of this convergence and to give effective a priori and aposteriori
error estimates in terms of a scalar function that is constructed on the base
of estimates for properties of invertibility and smoothness of linearizations
of the left-hand side of the equations under study. The principle is applicable
for analysis of such classical methods as method of minimal residuals, method
of steepest descent, method of minimal errors and others. The main results are
obtained for operator equations on Hilbert spaces and Banach spaces with a
special property, that is called Bynum property.
