Magic Efficiency of the Approximation of Smooth Functions by Weighted Means of Two N-Point Padé Approximants
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We consider the approximation of smooth functions by two weighted N-point Padé approximants and present some numerical examples and the inequalities between the Stieltjes function and its N-point Padé approximant.
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- 5.J. Gilewicz, “Approximants de Padé,” Lect. Notes Math., 667 (1978).Google Scholar
- 8.J. Gilewicz and R. Jedynak, “Compatibility of continued fraction convergents with Padé approximants,” in: Approximation and Computation. In Honor of Gradimir Milovanović. Most Papers Based on the Presentations at the International Conference, Niš, Serbia, August 25–29, 2008: Springer Optim. and Appl., Springer-Verlag (2010), pp. 135–144.Google Scholar
- 9.A. P. Holub and L. O. Lysenko, “Padé approximants for some classes of multivariate functions,” Ukr. Mat. Zh., 69, No. 5, 631–640 (2017); English translation : Ukr. Mat. J., 69, No. 5, 734–745 (2017).Google Scholar
- 11.R. Jedynak, “New facts concerning the approximation of the inverse Langevin function,” J. Non-Newton. Fluid Mech., 249 (2017).Google Scholar
- 12.R. Jedynak and J. Gilewicz, “Approximation of the integrals of the Gaussian distribution of asperity heights in the Greenwood–Tripp contact model of two rough surfaces revisited,” J. Appl. Math., 2013 (2013), Article ID 459280.Google Scholar
- 13.R. Jedynak and J. Gilewicz, “Approximation of smooth functions by weighted means of N-point Padé approximants,” Ukr. Math. Zh., 65, No. 10, 1410–1419 (2014); English translation : Ukr. Math. J., 65, No. 10, 1566–1576 (2014).Google Scholar
- 14.R. Jedynak and J. Gilewicz, “Computation of the c-table related to the Padé approximation,” J. Appl. Math., 2013 (2013), Article ID 185648.Google Scholar
- 17.O. M. Lytvyn and V. L. Rvachev, Taylor’s Classical Formula, Its Generalization and Application [in Ukrainian], Naukova Dumka, Kiev (1973).Google Scholar
- 21.J. Takacs, Hysteresis loop reversing by applying Langevin approximation,” COMPEL—Int. J. Comput. Math. Electr. Electron. Eng., 36, Issue 4, 850–858 (2017).Google Scholar