Abstract: | We investigate the approximation by manifolds n() generated by linear combinations of n radial basis functions on Rd of the form (|–a|), where is the thin-plate spline type function. We obtain exact asymptotic estimates for the approximation of Sobolev classes Wr(Bd) in the space L(Bd) on the unit ball Bd.AMS subject classification 41A25, 41A63, 65D07, 41A15 |