A reduced basis method for fractional diffusion operators I

Abstract We propose and analyze new numerical methods to evaluate fractional norms apply powers of elliptic operators. By means a reduced basis method, we project small dimensional subspace where explicit diagonalization via the eigensystem is feasible. The method relies on several independent evaluations $$({{\,\mathrm{I}\,}}-t_i^2\Delta )^{-1}f$$ ( I - t i 2 ? ) 1 f , which can be computed in parallel. prove exponential convergence rates for optimal choice sampling points $$t_i$$ provided by so-called Zolotarëv . Numerical experiments confirm analysis demonstrate efficiency our algorithm.