Lek-Heng Lim

Lek-Heng Lim is a mathematician from Singapore who specializes in numerical mathematics.

Lim studied mathematics from 1993 at the National University of Singapore with a bachelor's degree in 1996 and then at Cornell University , where he received his master's degree in 2000. In 2000/2001 he was a Clare Hall Fellow at Cambridge University . In 2007 he received his PhD from Stanford University with Gene Golub and Gunnar Carlsson . In 2007 he became Charles B. Morrey Assistant Professor at the University of California, Berkeley and in 2010 Assistant Professor and 2017 Associate Professor at the University of Chicago .

He deals with numerical linear algebra, for example (hyper) matrix and tensor calculations. With K. Ye he developed the fastest algorithm for vector matrix multiplication for Toeplitz and Hankel matrices. In continuation of the work of Volker Strassen , he investigated the role of the tensor rank in the numerical complexity of multilinear algebra (and especially the nuclear tensor norm for numerical stability). With C. Hillar he proved that almost all tensor problems are NP-hard. With Vin de Silva he showed that the problem of the best approximation of low order is ill-posed for tensors of order 3 and higher (the approximations sought do not need to exist). Among other things, he examined image analysis for magnetic resonance images of nerve tracts in the brain as applications. He also applies topology methods, for example to the reconstruction of three-dimensional images from two-dimensional projections in cryo-electron microscopy.

In 2017 he received the James H. Wilkinson Prize and the Stephen Smale Prize from the Foundation of Computational Mathematics. For 2020 he was awarded the Hans Schneider Prize .

He is on the editorial board of Linear Algebra and its Applications and Linear and Multilinear Algebra .

Fonts (selection)

• Singular values ​​and eigenvalues ​​of tensors: a variational approach, Proceedings of IEEE Workshop on Computational Advances in Multisensor Adaptive Processing, Volume 1, 2005, pp. 129-132, Arxiv
• with P. Comon, G. Golub, B. Mourrain: Symmetric tensors and symmetric tensor rank, SIAM Journal on Matrix Analysis and Applications, Volume 30, 2008, pp. 1254-1279, Arxiv
• with V. De Silva: Tensor rank and the ill-posedness of the best low-rank approximation problem, SIAM Journal on Matrix Analysis and Applications, Volume 30, 2008, pp. 1084-1127, Arxiv
• with Comon: Multiarray Signal Processing: Tensor decomposition meets compressed sensing, Arxiv 2010
• with X. Jiang, Y. Yao, Y. Ye: Statistical ranking and combinatorial Hodge theory, Mathematical Programming, Volume 127, 2011, pp. 203-244
• with CJ Hillar: Most tensor problems are NP-hard, Journal of the ACM, Volume 60, 2013, p. 45, Arxiv
• Tensors and hypermatrices, in: Handbook of Linear Algebra, CRC Press 2013, pp. 231-260

Web links

• Homepage

Individual evidence

1. ^ Ye, Lim, Cohomology of Cryo-Electron Microscopy, Arxiv 2016
2. ↑ Wilkinson Prize 2017, SIAM, with interview
3. ^ Smale Prize for Lim