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 4-point transformation technique. Representation of the polynomial via basic elements gives a lever at solving various tasks of applied mathematics. So, in the polynomial approximation and smoothing problems the BEM presentation allows one to reduce the computational complexity of algorithms and increase their stability for error by choosing the internal relationship structure between variable and control parameters.
Keywords:data smoothing, least squares method, approximation by polynomials, linear regression, 4-point transformation, efficiency of algorithms.
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