Approximation of functions of two variables by harmonic splines

We construct two-dimensional splines and give two versions of an estimate of the deviation of splines from approximated functions. We compare approximations by a planar broken line and by a harmonic spline. We also substantiate the advisability of introduction of the notion of harmonic splines in mathematics.Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1190–1196, September, 1995.