Error Bounds for Kernel-Based Numerical Differentiation
Oleg Davydov, Strathclyde University (Scotland)
Location: Stevenson 1307
The literature on meshless methods observed that kernel-based numerical differentiation formulae are highly accurate and robust. We present error bounds for such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds for kernel-based interpolation but are not applicable in this setting. Since differentiation formulas based on polynomials also have error bounds in terms of growth functions, we show that kernel-based formulas are comparable in accuracy to the best possible polynomial-based formulas. The talk is based on joint research with Robert Schaback.