Expansion over a system of shifts of pyramidal functions / T. P. Lukashenko, S. M. Lytkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 4. P. 22-28 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 159-164].
A method for approximation of functions of two variables by a linear combination of nonnegative piecewise linear functions with a compact support is presented. The crucial idea of this method consists in an "integral" calculation method for the coefficients. The accuracy of the approximation in the spaces of continuous and integrable functions is proved to have the same order as the best approximation by piecewise linear functions.
Key words: piecewise linear function of two variables, compact support, "integral" coefficients.