  In this paper, we show that the classical discrete orthogonal univariate
polynomials (namely, Hahn polynomials on an equidistant lattice with unit
weights) of sufficiently high degrees have extremely small values near the
endpoints (we call this property as "rapid decay near the endpoints of the
discrete lattice". We demonstrate the importance of the proved results applying
polynomial least squares approximation for the detection of anomalous values in
IGS final orbits for GPS and GLONASS satellites. We propose a numerically
stable method for the construction of discrete orthogonal polynomials of high
degrees. It allows one to reliably construct Hahn-Chebyshev polynomials using
standard accuracy (double precision, 8-byte) on thousands of points, for
degrees up to several hundred. A Julia implementation of the mentioned
algorithms is available at
https://github.com/sptsarev/high-deg-polynomial-fitting.
  These results seem to be new; their explanation in the framework of the
well-known asymptotic theory of discrete orthogonal polynomials could not be
found in the literature.
