Lecture 2

Example
The function
U(x1, . . . , x d) = x1 + . . . + x d ∈ H
in canonical representation
U(x1, . . . , x d) = x1 · 1 · .. · 1 + 1 · x2 · 1 · .. · 1 + . . . + 1 · .. · 1 · x d
In Tucker format, let
U i,1 = 1, U i,2 = x i be the basis of U i (non-orthogonal), r i = 2.
U inTT or MPS representation
U(x) = x1 + . . . + xd = � x1 1 � � �
1 0
· . . . ·
x2 1
(non-orthogonal), r1 = . . . = r d−1 = 2
� � � �
1 0 1
.
xd−1 1 xd