Abstract of Dmitry Savostyanov

Operations in Tucker format with applications in quantum chemistry
We consider approximate multiplication of matrices

D ≈ C = A * B

with A and B given as Tucker decomposition with mode ranks r and * denotes any linear operation. The matrix C does not appear as full array or as Tucker decomposition with mode ranks r2. Instead C is directly approximated by D in Tucker format with optimal values of ranks possible within a desired accuracy bound by independent factor filtering and a modified Tucker-ALS procedure. We also propose a fast initialization of Tucker-ALS by estimation of Tucker factors from Gram matrices of certain ''partionings'' of the tensor. Numerical examples include the structured evaluation of typical operators from the Hartree-Fock/Kohn-Sham model by means of Canonical-to-Tucker and Tucker-to-Tucker multiplication.


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