## Preliminary list of abstracts

Note: We are using the fantastic MathJax JavaScript library to typeset the mathematics on this web page. You can right-click on a formula to zoom in or to select the rendering engine you like (all under 'Settings'). Under Firefox the default renderer turns out to be MathML (which is quick), but you might prefer the HTML-CSS renderer for more faithful LaTeX rendering. If you encounter any problems with this setup: then please email us!

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.