Abstract of Boris Khoromskij

Quantics Approximation of N-d Tensors in High-Dimensional Applications
We discuss the novel concept of super-compressed tensor-structured data formats well suited in high dimensional applications. It is based on the multi-folding or quantics representation of multidimensional data arrays. Low rank tensor decomposition via the TT-type dimension splitting schemes leads to logarithmic scaling in the volume size. Numerical illustrations indicate that the quantics tensor method has proved its value in application to various function related tensors arising in quantum chemistry and in the traditional FEM/BEM---the tool apparently works. In particular, this method can be applied in the framework of truncated iteration for solution the high dimensional elliptic/parabolic problems.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)