Dresden Mathematical Seminar by Prof. Michael Hecht, CASUS Young Investigator Group Leader

Abstract of the talk// Michael will introduce a fast Newton interpolation algorithm with a runtime complexity of O(Nn), where N denotes the dimension of the underlying downward closed polynomial space and n its lp-degree, where p > 1. He will demonstrate that the algorithm achieves the optimal geometric approximation rate for analytic Bos-Levenberg-Trefethen functions in the hypercube. In this case, the Euclidean degree p = 2 emerges as the pivotal choice for mitigating the curse of dimensionality. The spectral differentiation matrices in the Newton basis are sparse, enabling the implementation of fast pseudo-spectral methods on flat spaces, polygonal domains, and regular manifolds.

In particular, Michael revisit his former contribution, entitled “Global Polynomial Level Sets (GPLS) for Numerical Differential Geometry of Smooth Closed Surfaces”. The GPLS provides an approximation for a wide range of smooth surfaces, which are initially given solely as point clouds, using a global polynomial level set. This enables efficient and accurate computation of various differential-geometric quantities, such as mean and Gauss curvature, or even higher-order terms like the Laplacian of mean curvature, in a straightforward manner. The GPLS significantly reduces the number of surface points required compared to classic alternatives that rely on surface meshes or embedding grids. He then will sketch extensions to higher dimensions, and discuss applications in numerical differential geometry.

Venue// Lecture room at Willers-Bau, Room C 129, TU Dresden, Zellescher Weg 12 – 14, 01069 Dresden (link)

Michael will be talking live in Dresden. Videoconferencing opportunities are not available.