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Application of a continuant to the estimation of a remainder term of Thiele’s interpolation continued fraction. (English. Ukrainian original) Zbl 1475.41002

J. Math. Sci., New York 246, No. 5, 687-700 (2020); translation from Ukr. Mat. Visn. 16, No. 4, 588-603 (2019).
This paper studies the problem of interpolation of functions of a real variable by means of Thiele’s interpolation continued fraction. The author obtains the formula for the remainder term of Thiele’s interpolation continued fraction and provides its estimate. Several numerical examples illustrate the advantages of the new estimate of the remainder term over previous work.

MSC:

41A05 Interpolation in approximation theory
41A80 Remainders in approximation formulas
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