Rational Chebyshev approximations for the inverse of the error function

Authors:
J. M. Blair, C. A. Edwards and J. H. Johnson

Journal:
Math. Comp. **30** (1976), 827-830

MSC:
Primary 65D20; Secondary 33A20

MathSciNet review:
0421040

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This report presents near-minimax rational approximations for the inverse of the error function inverf *x*, for , with relative errors ranging down to . An asymptotic formula for the region is also given.

**[1]**L. F. SHAMPINE, "Exact solutions for concentration dependent diffusion and the inverse complementary error function,"*J. Franklin Inst.*, v. 295, 1973, pp. 239-247.**[2]**Mervin E. Muller,*An inverse method for the generation of random normal deviates on large-scale computers*, Math. Tables Aids Comput.**12**(1958), 167–174. MR**0102905**, 10.1090/S0025-5718-1958-0102905-1**[3]**E. L. BATTISTE & T. P. YEAGER, "GGNOR-generate pseudo-normal random numbers,"*IMSL Library*3*Reference Manual*, v. 1, 1974**[4]**J. R. Philip,*The function inverfc 𝜃*, Austral. J. Phys.**13**(1960), 13–20. MR**0118857****[5]**Cecil Hastings Jr.,*Approximations for digital computers*, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR**0068915****[6]**P. KINNUCAN & H. KUKI,*A Single Precision Inverse Error Function Subroutine*, Computation Center, Univ. of Chicago, 1970.**[7]**Anthony Strecok,*On the calculation of the inverse of the error function*, Math. Comp.**22**(1968), 144–158. MR**0223070**, 10.1090/S0025-5718-1968-0223070-2**[8]**J. H. JOHNSON & J. M. BLAIR,*REMES*2-*A FORTRAN Program to Calculate Rational Minimax Approximations to a Given Function*, Report AECL-4210, Atomic Energy of Canada Limited, Chalk River, Ontario, 1973.**[9]**I. D. HILL & S. A. JOYCE, "Algorithm 304. Normal curve integral [S15],"*Comm. A.C.M.*, v. 10, 1967, pp. 374-375.**[10]**J. F. HART et al.,*Computer Approximations*, Wiley, New York, 1968.**[11]**C. Mesztenyi and C. Witzgall,*Stable evaluation of polynomials*, J. Res. Nat. Bur. Standards Sect. B**71B**(1967), 11–17. MR**0212994**

Retrieve articles in *Mathematics of Computation*
with MSC:
65D20,
33A20

Retrieve articles in all journals with MSC: 65D20, 33A20

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0421040-7

Keywords:
Rational Chebyshev approximations,
inverse error function,
minimal Newton form

Article copyright:
© Copyright 1976
American Mathematical Society