Lecture 2

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Hierarchical Tucker tensors ⊲ Canonical decomposition ⊲ Subspace approach (Hackbusch/Kühn, 2009) (Example: d = 5, U i ∈ R n×k i , Bt ∈ R kt ×kt 1 ×kt 2 )
Hierarchical Tucker tensors ⊲ Canonical decomposition not closed, no embedded manifold! ⊲ Subspace approach (Hackbusch/Kühn, 2009) (Example: d = 5, U i ∈ R n×k i , Bt ∈ R kt ×kt 1 ×kt 2 )
Page 1 and 2: Tensor networks, TT (Matrix Product
Page 3 and 4: Contracted tensor representations E
Page 5 and 6: Contracted tensor representations D
Page 7 and 8: Tensor networks Diagramm: u [x] Dia
Page 9 and 10: Tensor formats ⊲ Hierarchical Tuc
Page 11 and 12: Tensor formats ⊲ Hierarchical Tuc
Page 13 and 14: TT approximations of Friedman data
Page 15 and 16: Hierarchical Tucker as subspace app
Page 17: Orthonormal basis and recursive des
Page 21 and 22: Hierarchical Tucker tensors ⊲ Can
Page 23 and 24: Hierarchical Tucker tensors ⊲ Can
Page 25 and 26: HOSVD bases (Hackbusch) 1) Assume r
Page 27 and 28: Successive SVD for e.g. TT tensors
Page 29 and 30: Successive SVD for e.g. TT tensors
Page 31 and 32: Closedness A tree T D is characteri
Page 33 and 34: Summary For Tucker and HT redundanc

Lecture 2

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