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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0310505-7
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.


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Keywords: Approximation theory, rational approximation, approximation of entire functions, geometric convergence
Article copyright: © Copyright 1972 American Mathematical Society