Multivariate approximation at huge scattered meshes

The paper deals with the "true" multi-dimensional interpolation problem at scattered meshes with a huge number of interpolating points. For its solution we suggest here a new numerical technology consisting in partitioning of the problem on a number of subproblems and in a successive glueing of solutions to the subproblems. The basis of the partitioning method is the algorithm of optimal hyperplane, dividing a mesh in two intersected ones.