Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...

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Problem 6.6. Compare the efficiency of MyTucker3 and tucker als. Problem 6.7. Do cp als(A,1) and tucker als(A,1) return the same rank-1 tensor? ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 6. The Tucker Representation
More on Tensor Rank k-Rank If A ∈ IR n1×···×nd and 1 ≤ k ≤ d, then its k-rank is defined by rankk(A) = rank(A (k)) Problem 6.8. Show that if A ∈ IR n1×···×n d then there exists X = [[ S ; U1, . . . , Ud]] where for k = 1:d, Uk ∈ IR n k ×r k has orthonormal columns and rk = rankk(A). This can be thought of as a “thin” HOSVD. ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 6. The Tucker Representation
Page 1 and 2: From Matrix to Tensor: The Transiti
Page 3 and 4: What is This Lecture About? Approxi
Page 5 and 6: What is This Lecture About? The Pla
Page 7 and 8: The Tucker Product Representation (
Page 13 and 14: Matlab Tensor Toolbox: Tucker Tenso
Page 15 and 16: The Tucker Product Approximation Pr
Page 17 and 18: The Truncated HOSVD Look at A ≈ A
Page 19 and 20: Problem 6.2. Does this inequality h
Page 25 and 26: Alternating Least Squares Framework
Page 27 and 28: The Order-d Case The Tucker Product
Page 29: Matlab Tensor Toolbox: The Function
Page 33 and 34: Problem 6.9. Does it follow that th

Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...

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