The SIAM Student Chapter of Magdeburg is an association of students at the Otto-von-Guericke University and the Max Planck Institute in Magdeburg. Being part of the SIAM Chapter means having opportunities to develop networks with students from different faculties, departments, and research fields. This cooperation allows us to share ideas and research with people having similar interests,...
We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be the case for polynomial matrices expressed in the monomial basis. If the rational matrix has a particular self-conjugate structure we show how to construct strongly minimal linearizations that preserve it. The...
I consider the range-separated (RS) tensor format in numerical modeling of many particle interactions. The main focus is on efficient calculation of electrostatic potential of bio-molecules. Both free space potential and the case of polarized media will be addressed. In particular, the regularization of the Poisson-Boltzmann equation will be considered and numerical illustrations will be presented.
First, I give a brief overview about some of my recent work regarding large-scale linear algebra, in particular systems of linear equations and matrix equations. Afterwards, I speak about what happens from a linear algebra viewpoint when we allow polynomial nonlinearities in the systems.
Ill-posed problems require regularization to be solved. That is, it is necessary to project the problem onto a suitable subspace damping the influence of small singular values. Adaptive cross approximation is capable to identify low-rank approximations and, thus, reduce the number of small singular values.
In the talk we will demonstrate that this in fact works and what is needed...
The field of Natural Language Processing (NLP) has been undergoing a revolution in recent years. Large-scale language models (LLMs), most notably a series of Generative Pre-trained Transformers (GPTs), exceeded all expectations in benchmark scenarios and real life applications such as text generation, translation, question-answering and summarization.
The engine of the NLP revolution is the...
