Error Analysis and Resolution of Disagreements
Proper error analysis requires a very dense set of test points in R.
For power series expansion, it is possible to compute an exact upper bound on the error, and this should be done.
Testing should be done over the entire region of application using a very large and dense set of test points – this will insure sampling away from zeros of the error function, and will also validate the analytical error analysis and help find possible coding errors.
The three representations shown on a previous slide, while appearing to be different, may be equivalent in the following sense:
- Suppose that the test region for a set of ERMs is bounded and closed.
- e.g., R = [min. lon. , max. lon.] ? [min lat. , max. lat.] ? [min. ?, max. ?], where ? is the eccentricity of the set of meridian ellipses being considered.
- Then generate a dense grid on the three-dimensional region R.
- Then compare the three alternatives at each grid point.
- If the maximum absolute difference between them is less than some acceptable value (e.g., one millimeter), then they have equivalent accuracy.