Tensor-based Methods

Abstract

There are situations in which the size of the system is so large that it is impossible to store the vectors in full format. The data size may take values like Instead one needs sparse representations for all quantities The numerical tensor calculus offers very efficient tools for this purpose. In Section 14.1 we introduce tensor spaces and show typical examples. The key for the efficient numerical treatment is a suitable sparse tensor representation. In Section 14.2 we briefly define the r-term format, the subspace format as well as the hierarchical format. The inverse matrix approximated in §14.2.2.3 will play an important role as preconditioner. In Section 14.3 two different types of huge linear systems are described together with the definition of the truncated iteration for their solution. Finally, in Section 14.4, the variational approach and the alternating least squares method are mentioned.