Approximation of functions and quadrature formulas
Brief bases of the theory of spline-schemes, exact on polynomials are given. Recurrent schemes of construction of polynomial splines are considered. In conditions equally spaced measurements and gaussian models of an error are offered recurrent schemes, in a limit conterminous to the decision to a least square filtration.
For a case with enough smooth functions are studied schemes with an advancing (forecasting of value of a spline for a step forward).
In all considered cases are proved asymptotical stability and convergence of the constructed computing algorithms, estimations of a dispersion of deviations are received.
Results of numerical experiments are submitted.
Note. Abstracts are published in author's edition
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