Lecture 2

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Solution of −∆U = b ◮ Dimension d = 4, . . . , 128 varying ◮ Gridsize n = 10 ◮ Right-hand-side b of rank 1 ◮ Solution U has rank 13
Hierarchical Tucker as subspace approximation 1) D = {1, . . . , d}, tensor space V = � j∈D V j 2) T D dimension partition tree, vertices α ∈ T D are subsets α ⊂ T D, root: α = D 3) Vα = � j∈α V j for α ∈ T D 4) Uα ⊂ Vα subspaces of dimension rα with the characteristic nesting Uα ⊂ Uα1 ⊗ Uα2 (α1, 5) v ∈ U D (w.l.o.g. U D = span (v)). α2 sons of α)
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: TT approximations of Friedman data
Page 17 and 18: Orthonormal basis and recursive des
Page 19 and 20: 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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