27 citations · 44 across the 20 of their papers we have counts for
6 papers · 1 filter
On the Fractional Derivatives of Radial Basis Functions
Maryam Mohammadi, Robert Schaback
The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Ga…
Adaptive Approximation of Functions with Discontinuities
Licia Lenarduzzi, Robert Schaback
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth…
Error Analysis of Nodal Meshless Methods
Robert Schaback
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate der…
Optimal Stencils in Sobolev Spaces
Oleg Davydov, Robert Schaback
This paper proves that the approximation of pointwise derivatives of order of functions in Sobolev space by linear combinations of function values cannot have a c…
Minimal Numerical Differentiation Formulas
Oleg Davydov, Robert Schaback
We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of…
Superconvergence of Kernel-Based Interpolation
Robert Schaback
It is well-known that univariate cubic spline interpolation, if carried out on point sets with fill distance , converges only like in for functions in…