Plenary talk of Lars Eldén (University Linköping)

Computing Low-Rank Approximations of Sparse Tensors using Krylov Methods
Analyses of data organized as matrices are ubiquitous and well supported by theory and algorithms. For large and sparse matrices the main class of algorithms is Krylov methods. In many applications data are organized in more than two categories, and it is often unnatural to reorganize the data as a matrix. Thus there is a need for theory and algorithms for tensor computations. In many applications, especially in information sciences, the tensors are large and sparse. Recently we have discovered how to generalize matrix Krylov methods for the computation of low-rank approximations of tensors. We present different alternative ways of applying the Krylov idea to tensors. We also discuss how the low-rank approximation can be refined using a Krylov-Schur algorithm. Finally the use of tensor methods in a couple of areas in data mining is illustrated.
This is joint work with Berkant Savas.


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