Abstract:
The interpolation by means of real simplest fractions is considered. There are offered a different ways of intepolating simpest fractions construction with distinct real nodes. Necessary and sufficient conditions of existence and uniqueness of interpolating simplest fractions are received. Interpolation of constants is in detail investigated; in this case the estimation of an error of interpolation on Chebyshev's system of nodes is received.
Key words:
interpolation, simplest fractions.
Bibliographic databases:
Document Type:
Article
UDC:517.538.52, 517.538.7
Language: Russian
Citation:
E. N. Kondakova, “Interpolation by the simplest fractions”, Izv. Saratov Univ. Math. Mech. Inform., 9:2 (2009), 30–37
This publication is cited in the following 14 articles:
M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33
M. A. Komarov, “On approximation by special differences of simplest fractions”, St. Petersburg Math. J., 30:4 (2019), 655–665
V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Russian Math. (Iz. VUZ), 62:12 (2018), 6–41
M. A. Komarov, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Math. Notes, 104:6 (2018), 848–858
M. A. Komarov, “Best Approximation Rate of Constants by Simple Partial Fractions and Chebyshev Alternance”, Math. Notes, 97:5 (2015), 725–737
M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance”, Izv. Math., 79:3 (2015), 431–448
M. A. Komarov, “An Analog of the Haar Condition for Simple Partial Fractions”, J Math Sci, 208:2 (2015), 174
M. A. Komarov, “A criterion for the solvability of the multiple interpolation problem by simple partial fractions”, Siberian Math. J., 55:4 (2014), 611–621
M. A. Komarov, “A Criterion for the Best Approximation of Constants by Simple Partial Fractions”, Math. Notes, 93:2 (2013), 250–256
M. A. Komarov, “Sufficient condition for the best uniform approximation by simple partial fractions”, J Math Sci, 189:3 (2013), 482
V. I. Danchenko, E. N. Kondakova, “Criterion for the appearance of singular nodes under interpolation by simple partial fractions”, Proc. Steklov Inst. Math., 278 (2012), 41–50
M. A. Komarov, “Interpolation of rational functions by simple partial fractions”, J Math Sci, 181:5 (2012), 600
M. A. Komarov, “Uniqueness of a simple partial fraction of best approximation”, J Math Sci, 175:3 (2011), 284
V. I. Danchenko, E. N. Kondakova, “Chebyshev's alternance in the approximation of constants by simple partial fractions”, Proc. Steklov Inst. Math., 270 (2010), 80–90
Citation in format AMSBIB
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