Compact representation of ephemerides by discrete uniform approximation.
E.Z.Khotimskaia
At present the most widespread methods of constructing compact
representations for astronomical ephemerides are interpolation in the
roots of a Chebyshev polinomial of appropriate degree and least-squares
or uniform approximations. From the theoretical viwpoint, uniform
approximation is surely known to be the best, but it is customarily to
think that the procedures of obtaining such approximation are too
cumbersome in comparison with the simple algirithms for interpolation
or least-squares approximation. However, the development of methods
allowing one to reduce the construction of uniform approximation to
problems of linear programming has changed the situation completely.
In connection with the problem of discrete approximation of
astronomical ephemerides, in the present work it is shown that uniform
approximation has practical advantages as compared with least-squares
one. An exact estimate is obtained for the ratio of the maximum errors
of descrete least-squares and uniform polinomial approximations.