Abstract
It is shown that it is possible to apply a method proposed by V. K. Dzyadyk for the construction of rational functions that realize a near optimal approximation of entire elementary functions. The method may be termed linear in the sense that all the coefficients of the rational functions are determined from two systems of linear algebraic equations.
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References
V. K. Dzyadyk, “A-method in rational approximation,” Ukr. Mat. Zh.,37, No. 3, 250–252 (1985).
V. K. Dzyadyk, Approximate Methods for the Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1988), 303 pp.
V. K. Dzyadyk, “Effective construction of polynomials that realize near-optimal approximation of the functions ex, sin x, etc.,” Ukr. Mat. Zh.,25, No. 4, 435–453 (1973).
V. R. Kravchuk, “On effective approximation of elementary functions by means of rational functions of order (n, 1),” Ukr. Mat. Zh.,37, No. 2, 175–180 (1985).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 998–1000, July, 1992.
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Kravchuk, V.R. A simple method of rational approximation of functions. Ukr Math J 44, 903–905 (1992). https://doi.org/10.1007/BF01056147
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DOI: https://doi.org/10.1007/BF01056147