Eclipse predictions on this web site are based on j=2 ephemerides for the Sun [Newcomb, 1895] and Moon [Brown, 1919, and Eckert, Jones and Clark, 1954]. The value used for the Moon's secular acceleration is n-dot = -26 arc-sec/cy*cy, as deduced by Morrison and Ward .
The primary source of uncertainty in position of eclipse paths before 1000 CE is due to variations in Earth's rotation which is expressed through the parameter delta T. The value for delta-T was determined as follows:
1) pre-1600: delta T was derived from historical eclipse and occultation observations analyses by Stephenson 
2) 1600-present: delta T was obtained from published observations
3) future: delta-T was extrapolated from current values
Note that the predictions use a smaller value of k1 (=0.272281) than the one adopted by the 1982 IAU General Assembly (k=0.2725076). This results in a better approximation of Moon's minimum diameter and a slightly shorter total or longer annular eclipse when compared with calculations using the IAU value for k.
1k is the radius of the Moon expressed in units of Earth radii.
All eclipse calculations are by Fred Espenak, and he assumes full responsibility for their accuracy.
Permission is freely granted to reproduce this data when accompanied by an acknowledgment:
Eclipse Predictions & WebMaster: Fred Espenak
Planetary Systems Branch - Code 693