Lecture 2

Hierarchical Tucker tensors
⊲ Canonical decomposition not closed, no embedded
manifold!
⊲ Subspace approach (Hackbusch/Kühn, 2009)
U
1
B
{1,2}
U
2
B
{1,2,3}
U
3
U {1,2}
U {1,2,3}
B{1,2,3,4,5}
B
{4,5}
U4 U5
(Example: d = 5, U i ∈ R n×k i , Bt ∈ R kt ×kt 1 ×kt 2 )