Abstract of Jonas Ballani

A projection method to solve linear systems in tensor format
We propose a method for the numerical solution of a linear system of equations in tensor format. Such systems may arise from the discretisation of PDEs in high dimensions. We present an iterative scheme which is based on the projection of the residual to a low dimensional subspace. The subspace is spanned by vectors in tensor format of low rank which --- similarly to Krylov methods --- stem from the subsequent application of the given matrix to the residual. All calculations are performed in hierarchical Tucker format which results in a quadratic complexity in the dimension.


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