Computational Mathematics and Applications Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
23 November 2017
14:00
Professor Benedikt Wirth
Abstract

Spline curves represent a simple and efficient tool for data interpolation in Euclidean space. During the past decades, however, more and more applications have emerged that require interpolation in (often high-dimensional) nonlinear spaces such as Riemannian manifolds. An example is the generation of motion sequences in computer graphics, where the animated figure represents a curve in a Riemannian space of shapes. Two particularly useful spline interpolation methods derive from a variational principle: linear splines minimize the average squared velocity and cubic splines minimize the average squared acceleration among all interpolating curves. Those variational principles and their discrete analogues can be used to define continuous and discretized spline curves on (possibly infinite-dimensional) Riemannian manifolds. However, it turns out that well-posedness of cubic splines is much more intricate on nonlinear and high-dimensional spaces and requires quite strong conditions on the underlying manifold. We will analyse and discuss linear and cubic splines as well as their discrete counterparts on Riemannian manifolds and show a few applications.

  • Computational Mathematics and Applications Seminar
30 November 2017
14:00
Dr Vanessa Styles
Abstract

We analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Test calculations are presented that confirm our analysis.

  • Computational Mathematics and Applications Seminar
Professor James Nagy
Abstract


In this talk we describe an approach to approximate the truncated singular value decomposition of a large matrix by first decomposing the matrix into a sum of Kronecker products. Our approach can be used to more efficiently approximate a large number of singular values and vectors than other well known schemes, such as iterative algorithms based on the Golub-Kahan bidiagonalization or randomized matrix algorithms. We provide theoretical results and numerical experiments to demonstrate accuracy of our approximation, and show how the approximation can be used to solve large scale ill-posed inverse problems, either as an approximate filtering method, or as a preconditioner to accelerate iterative algorithms.
 

  • Computational Mathematics and Applications Seminar
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