Abstract
The basic element method (BEM) for decomposition of the algebraic polynomial via one cubic and three quadratic parabolas (basic elements) is developed within the four-point transformation technique. Representation of the polynomial via basic elements gives a lever for solving various tasks of applied mathematics. So, in the polynomial approximation and smoothing problems, the BEM allows one to reduce the computational complexity of algorithms and increase their resistance to errors by choosing an internal relationship structure between variable and control parameters.
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