Preliminary list of abstracts

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Spline interpolation on sparse grids
Keywords: spline; sparse grids; Besov spaces of mixed smoothness
Sun, 14:00--14:25
  • Ullrich, Tino (Hausdorff-Center for Mathematics, Institute for Numerical Simulation, University of Bonn, Germany)
  • Sickel, Winfried (Mathematical Institute, Department of Mathematics and Computer Science, University of Jena, Germany)

We investigate the rate of convergence of interpolating splines with respect to sparse grids for Sobolev-Besov spaces with mixed derivative on the cube $[0,1]^d$. In particular, we study the interpolation by tensor products of piecewise linear functions. The approximation is based on the Smolyak algorithm and uses only function samples taken from a sparse grid. Such a grid consists of considerably fewer grid points than the full cartesian product grid. The topic has been studied intensively in the last few decades and we were able to improve existing results significantly.