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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Convergence of best rational Tchebycheff approximations


Author: Barry Boehm
Journal: Trans. Amer. Math. Soc. 115 (1965), 388-399
MSC: Primary 41.17
MathSciNet review: 0199618
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  • [1] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956. MR 0095369 (20 #1872)
  • [2] J. L. Walsh, On approximation to an analytic function by rational functions of best approximation, Math. Z. 38 (1934), no. 1, 163–176. MR 1545445, http://dx.doi.org/10.1007/BF01170632
  • [3] Dunham Jackson, The theory of approximation, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR 1451140 (98a:01022)
  • [4] S. N. Bernstein, Sur l'ordre de la meilleure approximation des fonctions continues par des polynomes de degré donné, Mem. Acad. Belg. (2) 4 (1912), 1-103.
  • [5] J. L. Walsh, Über die Entwicklung einer Analytische Function nach Polynomen, Math. Ann. 96 (1926), 430-436.
  • [6] Ch. Muntz, Über den Approximationssatz von Weierstrass, Schwarz Festschrift (1914), 303-312.
  • [7] Barry Boehm, Functions whose best rational Chebyshev approximations are polynomials, Numer. Math. 6 (1964), 235–242. MR 0167759 (29 #5031)
  • [8] S. N. Bernstein, On the periodic functions for which the Fourier series is the best converging series (Russian, 1936); revised, Collected works, Moscow, 1954, pp. 178-183.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1965-0199618-7
PII: S 0002-9947(1965)0199618-7
Article copyright: © Copyright 1965 American Mathematical Society