  A method of modeling data with gaps by a sequence of curves has been
developed. The new method is a generalization of iterative construction of
singular expansion of matrices with gaps. Under discussion are three versions
of the method featuring clear physical interpretation: linear - modeling the
data by a sequence of linear manifolds of small dimension; quasilinear -
constructing "principal curves: (or "principal surfaces"), univalently
projected on the linear principal components; essentially non-linear - based on
constructing "principal curves": (principal strings and beams) employing the
variation principle; the iteration implementation of this method is close to
Kohonen self-organizing maps. The derived dependencies are extrapolated by
Carleman's formulas. The method is interpreted as a construction of neural
network conveyor designed to solve the following problems: to fill gaps in
data; to repair data - to correct initial data values in such a way as to make
the constructed models work best; to construct a calculator to fill gaps in the
data line fed to the input.
