FIXME: there is a problem with BRENT. The interval sometimes skips off
the root.  Somewhere the best guess is being used as the interval
endpoint which is wrong.

Add an inline version of the iterate method for speed? Perhaps not,
the time taken for each iteration surely dominated by the convergence
test.

-*-text-*- $Id: TODO,v 1.4 1999/07/20 16:06:16 bjg Exp $

This is a (hopefully complete) list of things which need to be done for the
root finding package. The ordering is random. Contact Reid (rp@lanl.gov) for
details or clarification on anything.

DONE * Add Brent and Dekker root finders. They are the best.

* Fix the documentation. It needs some minor reorganization and additions and
  some clarifications.

* Fix or trap the stopping problems in false position, secant method, and
  Newton's Method.

* Write the high level functions.

* Write a function to manufacture an fdf from an f and optionally a df. (We'll
  need to approximate the derivative if it is not provided; this is something
  which should be done outside the root finding package.)

* Write a function to extract f from an fdf.

* Verify and improve robustness. Write more tests. Bisection and the high
  level functions must be able to handle anything that we throw at them (they
  are allowed to give error messages when the input is invalid, but they must
  never give an incorrect answer (this is possible for bisection; is it
  possible for the high level function?); false position?, secant, and Newton
  are allowed to break, but we should minimize that and minimize especially
  wrong answers.

* Document in detail how everything can break. (To be done after breakage has
  been minimized.) 

* Make sure everything is portable (i.e. hook into Autoconf better).