The essential rate of approximation for radial function manifold (Q763668)

The authors investigated the radial function manifolds generated by a linear combination of radial functions. They assumed \(W_p^r(\mathbb{B}^d)\) to be the usual Sobolev class of functions on the unit ball \(\mathbb{B}^d\) and studied the deviation from the radical function manifolds to \(W_p^r(\mathbb{B}^d)\). Their results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical and also that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.