Polynomial Fitting of Data Streams with Applications to Codeword Testing

Andrew McGregor, Atri Rudra & Steve Uurtamo
Given a stream of $(x,y)$ points, we consider the problem of finding univariate polynomials that best fit the data. Over finite fields, this problem encompasses the well-studied problem of decoding Reed-Solomon codes while over the reals it corresponds to the well-studied polynomial regression problem. We present one-pass algorithms for two natural problems: i) find the polynomial of a given degree $k$ that minimizes the error and ii) find the polynomial of smallest degree that interpolates...