Chebyshev nodes in multiple dimensions by PhD candidate Sören Wolfers (KAUST)
Chebyshev nodes are well-known for their near-optimal polynomial interpolation and quadrature properties on intervals. In particular, the associated Lebesgue constant grows only logarithmically, whereas that associated to equispaced nodes grows exponentially.
Overview
Abstract
Chebyshev nodes are well-known for their near-optimal polynomial interpolation and quadrature properties on intervals. In particular, the associated Lebesgue constant grows only logarithmically, whereas that associated to equispaced nodes grows exponentially. Generalizations of Chebyshev nodes to domains in multiple dimensions have previously been studied on hyper-cubes only. In this talk, we consider more general domains and study the properties of node sets that are similar to Chebyshev nodes in the sense that they are distributed more densely near the boundary of the domain.
Brief Biography
Sören Wolfers received his BSc in Mathematics from the University of Heidelberg, Germany, in 2013 and will receive his MSc in Mathematics from the University of Bonn, Germany, in October 2015. He completed various research stays, for example at UCBL Lyon1, the Vision Lab at JHU, and the MPI in Göttingen. Since September 2015, Sören is a PhD student of Prof. Tempone at KAUST. His research interests include image processing, inverse problems and scattered data approximation. In particular, his master's thesis is on boundary effects in scattered data approximation.
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