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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Minimax approximations subject to a constraint
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by C. T. Fike and P. H. Sterbenz PDF
Math. Comp. 25 (1971), 295-298 Request permission

Abstract:

A class of approximation problems is considered in which a continuous, positive function $\varphi (x)$ is approximated by a rational function satisfying some identity. It is proved under certain hypotheses that there is a unique rational approximation satisfying the constraint and yielding minimax relative error and that the corresponding relative-error function does not have an equal-ripple graph. This approximation is, moreover, just the rational approximation to $\varphi (x)$ yielding minimax logarithmic error. This approximation, in turn, is just a constant multiple of the rational approximation to $\varphi (x)$ yielding minimax relative error but not necessarily satisfying the constraint.
References
    W. J. Cody & Anthony Ralston, "A note on computing approximations to the exponential function," Comm. ACM, v. 10, 1967, pp. 53-55.
  • I. F. Ganžela and C. T. Fike, Sterbenz, P. H, Math. Comp. 23 (1969), 313–318. MR 245199, DOI 10.1090/S0025-5718-1969-0245199-6
  • W. Kahan, "Library tape functions EXP, TWOXP, and .XPXP.," Programmers’ Reference Manual, University of Toronto, 1966. (Mimeographed.) W. J. Cody, "Double-precision square root for the CDC-3600," Comm. ACM, v. 7, 1964, pp. 715-718.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 295-298
  • MSC: Primary 41A20
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0303176-X
  • MathSciNet review: 0303176