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.
This publication is cited in the following 6 articles:
N. D. Dikusar, “Numerical solution of the Cauchy problem based on the basic element method”, Math. Models Comput. Simul., 15:6 (2023), 1024–1036
Korepanova N.V. Dikusar N.D. Pepelyshev Y.N. Dima M., “Neutron Noise Analysis Using the Basic Element Method”, Ann. Nucl. Energy, 131 (2019), 475–482
Robert M. Yamaleev, “Divided Differences Calculus in Matrix Representation”, Int. J. Appl. Comput. Math, 5:5 (2019)
Dikusar N., Mathematical Modeling and Computational Physics 2017 (Mmcp 2017), Epj Web of Conferences, 173, ed. Adam G. Busa J. Hnatic M. Podgainy D., E D P Sciences, 2018
N. D. Dikusar, “Polynomial approximation of the high orders”, Math. Models Comput. Simul., 8:2 (2016), 183–200
N. D. Dikusar, “Piecewise polynomial approximation of the sixth order with automatic knots detection”, Math. Models Comput. Simul., 6:5 (2014), 509–522
Citation in format AMSBIB
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