Expansion of pyramidal functions with square bottom over a shift system / *S. M. Lytkin.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 3. P. 3-7
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

A method for approximation of functions of two variables by a linear combination of nonnegative piecewise linear functions with a compact support is presented. Two quadratic pyramids are used as generating functions for the system of shifts. The accuracy of this local method 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, the best approximation.