Spline approximations on manifolds

A method of construction of the local approximations in the case of functions defined on n-dimensional (n >= 1) smooth manifold with boundary is proposed. In particular, spline and finite-element methods on manifold are discussed. Nondegenerate simplicial subdivision of the manifold is introduced and a simple method for evaluations of approach is examined (the evaluations axe optimal as to N-width of corresponding compact set).