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In this paper, we show that the classical discrete orthogonal univariatepolynomials (namely, Hahn polynomials on an equidistant lattice with unitweights) of sufficiently high degrees have extremely small values near theendpoints (we call this property as "rapid decay near the endpoints of thediscrete lattice". We demonstrate the importance of the proved results applyingpolynomial least squares approximation for the detection of anomalous values inIGS final orbits for GPS and GLONASS satellites. We propose a numericallystable method for the construction of discrete orthogonal polynomials of highdegrees. It allows one to reliably construct Hahn-Chebyshev polynomials usingstandard accuracy (double precision, 8-byte) on thousands of points, fordegrees up to several hundred. A Julia implementation of the mentionedalgorithms is available athttps://github.com/sptsarev/high-deg-polynomial-fitting.  These results seem to be new; their explanation in the framework of thewell-known asymptotic theory of discrete orthogonal polynomials could not befound in the literature.

Discrete orthogonal polynomials as a tool for detection of small anomalies of time series: a case study of GPS final orbits