L
Lek-Heng Lim
Researcher at University of Chicago
Publications - 126
Citations - 9445
Lek-Heng Lim is an academic researcher from University of Chicago. The author has contributed to research in topics: Tensor & Rank (linear algebra). The author has an hindex of 33, co-authored 115 publications receiving 8208 citations. Previous affiliations of Lek-Heng Lim include University of California, Berkeley & Stanford University.
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Most Tensor Problems Are NP-Hard
TL;DR: In this paper, it was shown that determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm, approximating an eigen value, eigenvector, singular vector, or the spectral norm is NP-hard and computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.
Journal ArticleDOI
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
Vin de Silva,Lek-Heng Lim +1 more
TL;DR: It is argued that the naive approach to this problem is doomed to failure because, unlike matrices, tensors of order 3 or higher can fail to have best rank-r approximations, and a natural way of overcoming the ill-posedness of the low-rank approximation problem is proposed by using weak solutions when true solutions do not exist.
Proceedings ArticleDOI
Singular values and eigenvalues of tensors: a variational approach
TL;DR: A theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigen values is proposed.
Posted Content
Tensor rank and the ill-posedness of the best low-rank approximation problem
Vin de Silva,Lek-Heng Lim +1 more
TL;DR: In this paper, it was shown that rank-1 tensors of order 3 or higher can fail to have the best rank-r approximations, regardless of the choice of norm (or even Bregman divergence).
Posted Content
Most tensor problems are NP-hard
TL;DR: It is proved that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard and how computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.