Abstract
The purpose of this paper is to call attention to a large body of results in the area of approximation by polynomials with integral coefficients. Those results with potential applications to the numerical aspects of the problem will be emphasized. By integral coefficients we mean coefficients from the ring of rational integers z = {...−1,0,1,...} and its generalizations. A detailed exposition of the general area of approximation by polynomials with integral coefficients will soon be available in Ferguson [1].
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References
L. B. O. Ferguson, Approximation by Polynomials with Integral Coefficients, Mathematical Surveys, American Math. Society, to appear.
G. G. Lorentz, Approximation of Functions, Athena Series, Holt, Rinehart and Winston, New York, 1966.
E. Hewitt and H. S. Zuckerman, “Approximation by polynomials with integral coefficients, a reformulation of the Stone-Weierstrass theorem,” Duke Math. J. 26 (1959), 305–324.
S. N. Bernšteǐn, “Some remarks on polynomials of least deviation with integral coefficients,” Dokl. Adad. Nauk SSSR, 4 (1930), 411–415. (Russian). Also: Sobranie Sočineniǐ: Tom 1, Konstruktivnaja Teorija Funktsiǐ (1905–1930), Moscow, 1952, 468–471; 562–563. (Russian) Translation: Collected Works: Vol. I, Constructive Theory of Functions (1905–1930), translated by the US Atomic Energy Commission, AEC-tr-3460, 140–144; 200–201.
L. V. Kantorovič, “Some remarks on the approximation of functions by means of polynomials with integral coefficients,” Izv. Akad. Nauk SSSR Ser Mat. (1931), 1163–1168. (Russian).
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Ferguson, L.B.O. (1978). Numerical Aspects of Approximation by Polynomials with Integral Coefficients. In: Collatz, L., Meinardus, G., Werner, H. (eds) Numerische Methoden der Approximationstheorie. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 42. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6460-2_8
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DOI: https://doi.org/10.1007/978-3-0348-6460-2_8
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