Geodesic
Various length step calculation method for piecewise linear approximation problem of empirical nonlinear function with a specified accuracy
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 35-48

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The paper proposes a numerical method for adaptive selection of a variable step for approximating a nonlinear one-dimensional function, the analytical expression of which is not given, by a piecewise linear function. It is shown that under the conditions of miniaturization of computing devices, the selection of the approximation step (grid) is an important task in terms of minimizing the required number of calculations. The developed algorithm includes the calculation of the lengths of successive intervals, which eventually cover the entire domain of the function, with a predetermined approximation accuracy. The coefficient of determination is used as a measure of accuracy. Numerical experiments are presented, the proposed method is compared with the method with a constant step, providing the same accuracy, also expressed in the value of the coefficient of determination. The conducted computational experiment proved the advantage of the developed method in terms of computational costs with the same accuracy.
Keywords: piecewise linear approximation, variable step, approximation grid step, numerical methods. 
@article{VTPMK_2022_3_a2,
     author = {Z. Z. Mingaliyev and S. V. Novikova and G. V. Moiseyev},
     title = {Various length step calculation method for piecewise linear approximation problem of empirical nonlinear function with a specified accuracy},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {35--48},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a2/}
}
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Z. Z. Mingaliyev; S. V. Novikova; G. V. Moiseyev. Various length step calculation method for piecewise linear approximation problem of empirical nonlinear function with a specified accuracy. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 35-48. http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a2/