Деякі аспекти екстраполяції на основі інтерполяційних многочленів: Fìz.-mat. model. ìnf. tehnol. 2021, 33:175-180

• Date: 2021
• Main Authors: Turbal, Yuriy, Bomba, Andriy, Turbal, Mariana, Alkaleg Hsen Drivi, Abd
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: прогноз; інтерполяція; екстрапополяція; многочлен; формула Н’ютона-Грегорі; біноміальні коефіцієнти; трикутник Паскаля
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/224
• Journal Title: Physico-mathematical modeling and informational technologies

The problem of extrapolation on the basis of interpolation polynomials is considered in the paper. A simple computational procedure is proposed to find the predicted value for a polynomial of any degree under conditions of a uniform grid. An algorithm for determining the best polynomial for extrapolation is proposed. To construction of integral transformation for operator of equation of convective diffusion under mixed boundary conditions. References Dzyadyk, V. K. (1958). “On the approximation of functions by ordinary polynomials on a finite segment of the real axis,” Izv. Academy of Sciences of the USSR. Ser. Mat., 22(3), 337–354. Turbal, Y., Bomba, A., Sokh, A., Radoveniuk, O., Turbal, M. (2019). Pyramidal method of small time series extrapolation. International journal of computing science and mathematic, 10(4), 122-130. DOI https://doi.org/10.1504/ijcsm.2019.104025 Bomba, A., Turbal, Y. (2015). Data analysis method and problems of identification of trajectories of solitary waves. Journal of Automation and Information Sciences, 5, 34-43. DOI https://doi.org/10.1615/jautomatinfscien.v47.i10.20 Kostinsky, A. S. (2014). On the principles of a spline extrapolation concerning geophysical data. Reports of the National Academy of Sciences of Ukraine, 111–117. DOI https://doi.org/10.15407/dopovidi2014.02.111 Zakharov, A. A. (2016). B-splines and B-spline surfaces. MSTU im. Bauman. Shalaginov, A. V. (2011). Cubic spline extrapolation of time series. UNK “IASA” NTUU “KPI”. Kiev. Volkov, E. A. (1967). “Remarks on the approximation of functions by polynomials,” Zh. Vychisl. mat. and mat. fiz., 7(6), 1374-1375. Zhan, Z., Yang, R., Xi, Z. (2012). A Bayesian Inference based Model Interpolation and Extrapolation. SAE Int. J. Mater. Manf., 5(2), 357-364. DOI https://doi.org/10.4271/2012-01-0223 Turbal, Y., Bomba, A., Sokh, A., Radoveniuk, O., Turbal, M. (2017). Spatial generalization of the pyramidal data etrapolation//Bulletin of Taras Shevchenko National University of Kyiv. Series Physics & Mathematics, 2, 146-151. DOI https://doi.org/10.1504/ijcsm.2019.104025 Turbal, Y., Turbal, M., Driwi, A. A., Al Shukri, S. (2020). On the equivalence of the forecast value construction in the “pyramidal” extrapolation method and cubic forecast, MCIT, 67–70. doi.org/10.31713/MCIT.2020.15 DOI https://doi.org/10.31713/mcit.2020.15 Monroe, J. I., Hatch, H. W., Mahynski, N. A., Shell, M. S., Shen, V. K. (2020). Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density. J. Chem. Phys. DOI https://doi.org/10.1063/5.0014282 Wang, L-Y., Lee, W-C. (2014). One-step extrapolation of the prediction performance of a gene signature derived from a small study. BMJ Open. DOI https://doi.org/10.1136/bmjopen-2014-007170 Bakas, N. P. (2019). Numerical Solution for the Extrapolation. Problem of Analytic Functions/Research. Makridakis, S., Bakas, N. (2016). Forecasting and uncertainty: a survey. Risk and Decision Analysis–v, 6(1), 37–64. DOI https://doi.org/10.3233/rda-150114 Demiris, N., Lunn, D., Sharples, L. D. (2015). Survival extrapolationusing the poly-Weibull model. Stat Methods Med Res., 24(2), 287–301. DOI https://doi.org/10.1177/0962280211419645