Zolotarev
Minmax rational approximation to the sign function
The programs in this package serve to compute the coefficients of
the optimal rational approximation of degree [2*n+1,2*n] to the sign
function. The approximating function is of the form
x*R(x2)
where R(y) is the (uniquely determined) rational function in y of
degree [n,n] that minimizes the error
max|1-sqrt(y)*R(y)|
in the range epsilon<=y<=1 for a specified value of
epsilon>0. R(y) thus approximates 1/sqrt(y) with uniform
relative error in this interval.
The optimization problem was solved analytically by Zolotarev a long
time ago. See
N.I. Achiezer,
Approximation Theory,
(Dover Publications, New York, 1992),
for example. There is another solution of the optimization problem,
where R(y) is taken to be a rational function of degree [n-1,n].
Both solutions are referred to as the Zolotarev rational
approximation to the sign function. Here only the slightly more
accurate [n,n] approximation is considered.
Download
The package
Zolotarev-1.0.tar.gz
contains the source programs, usage instructions and example main
programs. The programs are ISO C89 compliant and should compile and
execute correctly on any machine. After unpacking, first read the
README file in the top directory.
License
The software may be used under the terms of the
GNU General Public Licence (GPL)
.
Last updated 20 February 2015