An upper bound on the Lp-approximation power (1 p 1) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies to both stationary and non-stationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic splines, multiquadrics, and Gauss kernel.

We show how conditionally negative deenite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive deenite functions studied in 17] that closed form representations (as opposed to series expan...

Local radial basis functions (RBFs) have many advantages for solution of differential equations. In some these functions, there is a parameter that has special effect on the accuracy answer and known as shape parameter. this article, first all, we derive inverse quadratic (IQ)-based RBF-generated finite difference coefficients derivatives in one dimension (1D). Then, to evaluate efficiency new ...

This study makes the first attempt to apply the Kansa method in the solution of the time fractional diffusion equations, in which the MultiQuadrics and thin plate spline serve as the radial basis function. In the discretization formulation, the finite difference scheme and the Kansa method are respectively used to discretize time fractional derivative and spatial derivative terms. The numerical...