  It's well know that Radial Basis Function approximants suffers of bad
conditioning if the simple basis of translates is used. A recent work of
M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal
bases for the native space based on a factorization of the kernel matrix A.
Starting from that setting we describe a particular orthonormal basis that
arises from a weighted singular value decomposition of A. This basis is related
to a discretization of the compact operator which leads to the so-called
eigenbasis, and provides a connection with it. We give convergence estimates
and stability bound for the interpolation and the discrete least-squares
approximation based on this basis, which involves the eigenvalues of such an
operator.
