minimax rational functions
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§3.11(iii) Minimax Rational Approximations… ►Then the minimax (or best uniform) rational approximation … ►The theory of polynomial minimax approximation given in §3.11(i) can be extended to the case when is replaced by a rational function . … ►A collection of minimax rational approximations to elementary and special functions can be found in Hart et al. (1968). … ►
Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .
Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
§5.23(i) Rational Approximations►Cody and Hillstrom (1967) gives minimax rational approximations for for the ranges , , ; precision is variable. Hart et al. (1968) gives minimax polynomial and rational approximations to and in the intervals , , ; precision is variable. Cody et al. (1973) gives minimax rational approximations for for the ranges and ; precision is variable. … ►See Schmelzer and Trefethen (2007) for a survey of rational approximations to various scaled versions of . …
Moshier (1989, §6.14) provides minimax rational approximations for calculating , , , . They are in terms of the variable , where when is positive, when is negative, and when . The approximations apply when , that is, when or . The precision in the coefficients is 21S.