Abstract
We present a simple method for finding the values of the best approximation of a function of n variables of a given class by means of sums of two functions of a fewer number of variables; we establish close upper and lower bounds for the value of the best approximation to the functionf(x1, ..., xn), having the mixed derivativef x1 ... xn, by means of sums of a function of n−1 variables.
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Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 105–114, July, 1972.
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Babaev, M.B.A. On obtaining close estimates in the approximation of functions of many variables by sums of functions of a fewer number of variables. Mathematical Notes of the Academy of Sciences of the USSR 12, 495–500 (1972). https://doi.org/10.1007/BF01094399
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DOI: https://doi.org/10.1007/BF01094399