Editing Appendix/ComputerAlgorithms/EFE (section)

==jRoot2 (27 June 2016)==


File "jRoot2.for" calculates pairs of axis ratios that define
the Jacobi ellipsoid equilibrium sequence.

gfortran -o exroot jRoot2.o doubleELib.o

PROGRAM testnewt:  Loops through a group of 'c/a' axis ratios,
and for each one, relies upon FUNCTION rtnewt to return the
"root", which here is the matching value of 'b/a'.  In turn,
the function, rtnewt, calls the SUBROUTINE fJ, which provides
"rtnewt" with the definition of the governing relation for
Jacobi ellipsoids, as well as the analytic definition of the
first derivative of this function, with respect to 'b/a'.
The definitions of fJ and d(fJ)/dx are provided in our
[[ThreeDimensionalConfigurations/JacobiEllipsoids#Roots_of_the_Governing_Relation|accompanying discussion titled, "Roots of the Governing Relation"]].

FUNCTION rtnewt originated as a function drawn from the
Numerical Recipes collection of f77-formatted root-finding
algorithms; it uses the Newton-Raphson technique.  I modified
the original rtnewt in order to perform double-precision arithmetic.
The arguments of this FUNCTION are ...
<ul>
<li>covera = c/a;</li>
<li>x1 and x2 define the bracketed region of b/a within which the root should be found (if not, a message is written);</li>
<li>xacc = desired precision of root = b/a</li>
</ul>