4-Point transforms and approximation Original Research Article

The paper is devoted to the investigation of a recently proposed four-point transformation, the discrete projective transformation (DPT). Matrix transform equations of DPT and DPT of higher orders are derived for polynomials. The practical use of DPT and the derived equations is shown on a classic problem of regression analysis: a new approach is suggested for assessing the polynomial degree in fitting empirical data. The technique which does not need a computation of regression coefficients of the unknown polynomial, is illustrated on an example. The program implementation of DPT is accessible in a downloadable library of Maple functions.