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Spline Functions and Approximation Theory pp 31–56Cite as

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A Combinatorial Problem in Best Uniform Approximation

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Abstract

Given a function f of one variable, to minimize

$$ \left\| {f - g} \right\| = \mathop {\sup }\limits_t \left| {f(t) - g(t)} \right| $$

among all a which are monotonic on at mosst n sub-intervals

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References

  1. Bartholomew, D. J.: A test of homogeneity of means under restricted alternatives, J. Royal Statist. Soc. Ser. B23(1961), 239–273.

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  2. Davis, C.: Mapping properties of some Cebysev systems, Dokl. Akad. Nauk SSSR 175(1967), 280–283 = Soviet Math. Dokl. 7(1966), 1395–1398.

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  3. Kantorovic, L.V. and Rubinstein, G.S.: A space of completely additive functions, Vestnik Leningrad. Gos. Univ. 13(1958), no. 7, 52–59.

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  4. Krein, M.G.: The ideas of P.L. Cebysev and A.A. Markov in the theory of limiting values of integrals and their further development, Uspehi Mat. Nauk 6(1951), no. 4(44), 3–120 = Amer. Math. Soc. Transl. (2) 12(1959), 1–121.

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  5. Videnskii, V.S.: An existence theorem for the polynomial with a given sequence of extrema, Dokl. Akad. Nauk SSSR 171(1966), 17–20 = Soviet Math. Dokl. 7(1966), 1395–1398.

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Authors
  1. Chandler Davis
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Editor information

A. Meir A. Sharma

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© 1973 Springer Basel AG

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Davis, C. (1973). A Combinatorial Problem in Best Uniform Approximation. In: Meir, A., Sharma, A. (eds) Spline Functions and Approximation Theory. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 21. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5979-0_2

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  • DOI: https://doi.org/10.1007/978-3-0348-5979-0_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5980-6

  • Online ISBN: 978-3-0348-5979-0

  • eBook Packages: Springer Book Archive

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