Session B7 - Numerical Linear Algebra
July 13, 15:00 ~ 15:30 - Room B5
On the complexity of solving elliptic PDEs using low-rank tensor approximations
Universität Bonn, Germany - email@example.com
In the construction of solvers for high-dimensional problems based on hierarchical tensor representations, one faces a trade-off between ensuring convergence and retaining small ranks of arising intermediate quantities. When approximately solving PDEs, in addition, low-rank approximation errors need to be balanced with discretization errors. We give an overview of available results on the complexity of solvers for hierarchical tensor representations, as well as of some open questions. We also consider what can or cannot be gained by tensor methods applied to different classes of high-dimensional problems.
Joint work with Albert Cohen (UPMC Paris VI), Wolfgang Dahmen (RWTH Aachen) and Reinhold Schneider (TU Berlin).