  In this paper we present iterative methods of high efficiency by the criteria
of J. F. Traub and A. M. Ostrowski.
  We define {\it s-nonstationary iterative processes} and prove that, for any
one-point iterative process without memory, such as, for example, Newton's,
Halley's, Chebyshev's methods, there exists an s-nonstationary process of the
same order, but of higher efficiency.
  We supply constructions of these methods, obtain their properties and, for
some of them, also their geometric interpretation. The algorithms we present
can be transformed into computer programs in straight-forward manner. The
methods are demonstrated by numerical examples.
