Dynamics, numerical analysis, and some geometry
Numerical Analysis
2017-10-12 v1
Abstract
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic integrators for Hamiltonian ordinary and partial differential equations, of dynamical low-rank approximation of time-dependent large matrices and tensors, and its use in numerical integrators for Hamiltonian tensor network approximations in quantum dynamics.
Cite
@article{arxiv.1710.03946,
title = {Dynamics, numerical analysis, and some geometry},
author = {Ludwig Gauckler and Ernst Hairer and Christian Lubich},
journal= {arXiv preprint arXiv:1710.03946},
year = {2017}
}
Comments
prepared for the Proceedings of ICM 2018 (Christian Lubich's plenary talk)