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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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.
    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:
  • MathSciNet review: 0303176