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4-point transforms and approximation. (English) Zbl 0976.65011
The paper deals with a 4-point transformation – the discrete projective transformation (DPT) which was first proposed by N. D. Dikoussar [Comput. Phys. Commun. 79, 39-51 (1994)]. Considering the DPT of polynomials a DPT matrix is defined which allows the author to derive a matrix transform equation not only for the DPT but also for the DPT of higher orders. This makes the presentation of DPT and its computation more clear and simple. The method of using the DPT of higher orders for estimating the unknown degree of a polynomial in approximation by regression models is given. It is also mentioned that the generalisation of the new approach to strongly disturbed data and to the multidimensional case is under study.

MSC:
65D10 Numerical smoothing, curve fitting
65F20 Numerical solutions to overdetermined systems, pseudoinverses
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
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