Those familiar with the problems involved with error estimation
will appreciate the graphical error analysis performed on the Bessel
function (See web page below).
Bessel functions' analytical and numerical characteristics are well
documented (See A&S, G&R). When getting into the particulars
of the numerical evaluation of different algorithms, however, error
analyses are cumbersome and only partially available. Using the
capabilities of computer graphics, it is possible to visualize errors
and estimate their magnitude "empirically". To demonstrate the
power of this method, graphical error analysis of the proprietary
procedure _JaX that evaluates the Bessel Function of the First
Kind is performed.
Dan Baruth