Despite such very appealing features of the radial basis function (RBF) as inherent meshfree and independent of dimension and geometry, the various RBF-based schemes [1] of solving partial differential equations (PDE’s) still confront some deficiencies. For instances, the lack of easy-to-use spectral convergent RBFs, ill-conditioning and costly evaluation of full interpolation matrix. The purpo...

We study the necessary and sufficient conditions for the generation of polynomials by stationary subdivision schemes, and we show how to derive appropriate quasiinterpolation rules that have the optimal approximation order. We show that these conditions hold in the context of non-uniform subdivision as well, and we demonstrate how they can be used for the construction of stationary non-uniform ...