Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Converse theorems and extensions in Chebyshev rational approximation to certain entire functions in $ [\ast \ast \ast w(\ast \ast 0,\,+\infty )\ast \ast \ast w\ast \ast $


Authors: G. Meinardus, A. R. Reddy, G. D. Taylor and R. S. Varga
Journal: Trans. Amer. Math. Soc. 170 (1972), 171-185
MSC: Primary 41A20; Secondary 26A93
Addendum: Trans. Amer. Math. Soc. 186 (1973), 499-502.
MathSciNet review: 0310505
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Abstract: Recent interest in rational approximations to $ {e^{ - x}}$ in $ [0, + \infty )$, arising naturally in numerical methods for approximating solutions of heat-conduction-type parabolic differential equations, has generated results showing that the best Chebyshev rational approximations to $ {e^{ - x}}$, and to reciprocals of certain entire functions, have errors for the interval $ [0, + \infty )$ which converge geometrically to zero. We present here some related converse results in the spirit of the work of S. N. Bernstein.


References [Enhancements On Off] (What's this?)

  • [1] Ralph Philip Boas Jr., Entire functions, Academic Press Inc., New York, 1954. MR 0068627
  • [2] W. J. Cody, G. Meinardus, and R. S. Varga, Chebyshev rational approximations to 𝑒^{-𝑥} in [0, +∞) and applications to heat-conduction problems, J. Approximation Theory 2 (1969), 50–65. MR 0245224
  • [3] Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition. Translated by Larry L. Schumaker. Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. MR 0217482
  • [4] Günter Meinardus and Richard S. Varga, Chebyshev rational approximations to certain entire functions in [0,+∞), J. Approximation Theory 3 (1970), 300–309. MR 0280914
  • [5] A. F. Timan, Teorij pribli+enij funkcii deistvitel’nogo peremennogo, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1960 (Russian). MR 0117478
  • [6] G. Valiron, Lectures on the general theory of integral functions, Chelsea, New York, 1949.
  • [7] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
  • [8] -, Some results in approximation theory with applications to numerical analysis, Numerical Solution of Partial Differential Equations, vol. 2, Academic Press, New York, 1971, pp. 623-649.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310505-7
Keywords: Approximation theory, rational approximation, approximation of entire functions, geometric convergence
Article copyright: © Copyright 1972 American Mathematical Society