Converse theorems and extensions in Chebyshev rational approximation to certain entire functions in $[\ast \ast \ast w(\ast \ast 0, +\infty )\ast \ast \ast w\ast \ast$
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- by G. Meinardus, A. R. Reddy, G. D. Taylor and R. S. Varga PDF
- Trans. Amer. Math. Soc. 170 (1972), 171-185 Request permission
Addendum: Trans. Amer. Math. Soc. 186 (1973), 499-502.
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
- Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
- W. J. Cody, G. Meinardus, and R. S. Varga, Chebyshev rational approximations to $e^{-x}$ in $[0,$ $+\infty )$ and applications to heat-conduction problems, J. Approximation Theory 2 (1969), 50–65. MR 245224, DOI 10.1016/0021-9045(69)90030-6
- Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482
- Günter Meinardus and Richard S. Varga, Chebyshev rational approximations to certain entire functions in $[0,\,+\infty )$, J. Approximation Theory 3 (1970), 300–309. MR 280914, DOI 10.1016/0021-9045(70)90054-7
- A. F. Timan, Teorij pribli+enij funkciĭ deĭstvitel’nogo peremennogo, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1960 (Russian). MR 0117478 G. Valiron, Lectures on the general theory of integral functions, Chelsea, New York, 1949.
- Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502 —, 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.
Additional Information
- © Copyright 1972 American Mathematical Society
- 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
- MathSciNet review: 0310505