L.-H. Lim and K. Ye, "Minimal equivariant embeddings of the Grassmannian and
flag manifold," *preprint*, (2024).

L.-H. Lim and K. Ye, "Simple matrix models for the flag, Grassmann, and Stiefel
manifolds," *preprint*, (2024).

Z. Lai, L.-H. Lim, and Y. Liu, "Attention is a smoothed cubic spline,"
*preprint*, (2024).

Z. Lai, L.-H. Lim, and K. Ye, "Grassmannian optimization is NP-hard,"
*preprint*, (2024).

Z. Lai, L.-H. Lim, and K. Ye, "Simple matrix expressions for the curvatures of
Grassmannian,"
*preprint*, (2024).

L.-H. Lim and K. Ye, "Degree of the Grassmannian as an affine variety,"
*preprint*, (2024).

L.-H. Lim and B. Nelson, "What is … an equivariant neural network?,"
*Notices of the American Mathematical Society*, **70**
(2023), no. 4, pp. 619–625.

Y. Liu, S. Jiao, and L.-H. Lim, "LU decomposition and Toeplitz decomposition of a neural
network," *Applied and Computational
Harmonic Analysis*, **68** (2024), Art. 101601.

R. Wang, J. Lee, and L.-H. Lim, "Summing divergent matrix series,"
*preprint*, (2024).

Z. Dai and L.-H. Lim, "Numerical stability and tensor nuclear norm,"
*Numerische Mathematik*, **155** (2023), no. 3–4, pp.
345–376.

Z. Dai, L.-H. Lim, and K. Ye, "Complex matrix inversion via real matrix inversions,"
*preprint*, (2023).

Z. Li and L.-H. Lim, "Generalized matrix nearness problems,"
*SIAM Journal on Matrix Analysis and Applications*, **44** (2023),
no. 4, pp. 1709–1730.

Y. Cai and L.-H. Lim, "Distances
between probability distributions of different dimensions,"
*IEEE Transactions on Information Theory*, **68** (2022), no.
6, pp. 4020–4031.

Z. Lai, L.-H. Lim, and K. Ye, "Simpler Grassmannian optimization," *preprint*,
(2020).

Z. Lai and L.-H. Lim, "Recht–Ré noncommutative arithmetic-geometric
mean conjecture is false," *Proceedings of the 37th International
Conference on Machine Learning* (ICML), PMLR **119**, (2020),
pp. 5608–5617.

M. Zhao, Z. Lai, and L.-H. Lim, "Stochastic Steffensen method,"
*Computational Optimization and Applications*, **89** (2024), pp.
1–32.

S. Friedland and L.-H. Lim, "Symmetric Grothendieck inequality," *preprint*,
(2020).

L.-H. Lim, "Tensors in
computations," *Acta Numerica*, **30** (2021), pp.
555–764.

L.-H. Lim, M. Michałek, and Y. Qi, "Best *k*-layer
neural network approximations," *Constructive Approximation*,
**55** (2022), no. 1, pp. 583–604.

G. Naitzat, A. Zhitnikov, and L.-H. Lim, "Topology of deep neural networks,"
*Journal of Machine Learning Research*, **21** (2020), no.
184, pp. 1–40.

K. Ye, K. Wong, and L.-H. Lim, "Optimization on
flag manifolds," *Mathematical Programming*, **194** (2022),
no. 1–2, pp. 621–660.

T. Gao, L.-H. Lim, and K. Ye, "Semi-Riemannian
manifold optimization," *preprint*, (2018).

L. Ding and L.-H. Lim, "Higher-order cone
programming," *preprint*, (2018).

L.-H. Lim, R. Sepulchre, and K. Ye, "Geometric distance between positive definite
matrices of different dimensions," *IEEE Transactions on
Information Theory*, **65** (2019), no. 9, pp. 5401–5405.

J. Rodriguez, J.-H. Du, Y. You, and L.-H. Lim, "Fiber product homotopy method for multiparameter
eigenvalue problems," *Numerische Mathematik*, **148** (2021),
no. 4, pp. 853–888.

L. Zhang, G. Naitzat, and L.-H. Lim, "Tropical geometry of deep neural networks,"
*Proceedings of the 35th International Conference on Machine
Learning* (ICML), PMLR **80** (2018), pp. 5824–5832.

P. Comon, L.-H. Lim, Y. Qi, and K. Ye, "Topology of tensor ranks," *Advances in
Mathematics*, **367** (2020), no. 107128, 46 pp.

H. Derksen, S. Friedland, L.-H. Lim, and L. Wang, "Theoretical
and computational aspects of entanglement," *preprint*,
(2017).

S. Friedland, L.-H. Lim, and J. Zhang, "An elementary and unified proof of Grothendieck's
inequality," *Lâ€™Enseignement Mathématique*, **64**
(2018), no. 3/4, pp. 327–351.

L.-H. Lim, K. S.-W. Wong, and K. Ye, "The Grassmannian of affine subspaces,"
*Foundations of Computational Mathematics*, **21** (2021), pp.
537–574.

Y. Qi, M. Michałek, and L.-H. Lim, "Complex best *r*-term approximations almost always
exist in finite dimensions," *Applied and Computational
Harmonic Analysis*, **49** (2020), no. 1, pp. 180–207.

K. Ye and L.-H. Lim, "Tensor network
ranks," *preprint*, (2018).

M. Ankele, L.-H. Lim, S. Groeschel, and T. Schultz, "Versatile, robust, and efficient
tractography with constrained higher-order tensor fODFs,"
*International Journal of Computer Assisted Radiology and
Surgery*, **12** (2017), no. 8, pp. 1257–1270.

M. Ankele, L.-H. Lim, S. Groeschel, and T. Schultz, "Fast and accurate multi-tissue
deconvolution using SHORE and H-PSD tensors," pp. 502–510, S.
Ourselin et al. (Eds), *Medical Image Computing and Computer Assisted
Intervention* (MICCAI), **III**,
Springer International, Cham, 2016.

K. Ye and L.-H. Lim, "Cohomology of cyro-electron microscopy,"
*SIAM Journal on Applied Algebra and Geometry*, **1** (2017), no.
1, pp. 507–535.

Y. You, J. Rodriguez, and L.-H. Lim, "Accurate solutions of polynomial eigenvalue problems,"
*preprint*, (2017).

S. Friedland, L.-H. Lim, and J. Zhang, "Grothendieck constant is norm of Strassen matrix
multiplication tensor," *Numerische Mathematik*, **143**
(2019), no. 4, pp. 905–922.

A. Benson, D. Gleich, and L.-H. Lim, "The spacey random walk: a stochastic process for
higher-order data," *SIAM Review*, **59** (2017), no. 2, pp.
321–345.

L.-H. Lim and J. Weare, "Fast randomized iteration: diffusion Monte Carlo
through the lens of numerical linear algebra,"
*SIAM Review*, **59** (2017), no. 3, pp. 547–587. [Supplementary Materials]

Y. Qi, P. Comon, and L.-H. Lim, "Semialgebraic geometry of nonnegative tensor rank,"
*SIAM Journal on Matrix Analysis and Applications*, **37** (2016),
no. 4, pp. 1556–1580.

K. Ye and L.-H. Lim, "Algorithms for structured matrix-vector product of
optimal bilinear complexity," *Proceedings of the IEEE
Information Theory Workshop* (ITW), **16** (2016), pp.
310–314.

K. Ye and L.-H. Lim, "Fast
structured matrix computations: tensor rank and Cohn–Umans
method," *Foundations of Computational Mathematics*,
**18** (2018), no. 1, pp. 45–95.

S. Friedland and L.-H. Lim, "The computational complexity of duality,"
*SIAM Journal on Optimization*, **26** (2016), no. 4, pp.
2378–2393.

D. Gleich, L.-H. Lim, and Y. Yu, "Multilinear PageRank," *SIAM Journal on Matrix
Analysis and Applications*, **36** (2015), no. 4, pp.
1507–1541.

L.-H. Lim, "Hodge Laplacians
on graphs," *SIAM Review*, **62** (2020), no. 3, pp.
685–715.

L.-H. Lim, K. S.-W. Wong, and K. Ye, "Numerical algorithms on the affine Grassmannian,"
*SIAM Journal on Matrix Analysis and Applications*, **40** (2019),
no. 2, pp. 371–393.

Y. Qi, P. Comon, and L.-H. Lim, "Uniqueness of nonnegative tensor approximations,"
*IEEE Transactions on Information Theory*, **62** (2016), no. 4,
pp. 2170–2183.

S. Friedland and L.-H. Lim, "Nuclear norm of higher-order tensors,"
*Mathematics of Computation*, **87** (2018), no. 311, pp.
1255–1281.

L.-H. Lim, "Self-concordance is NP-hard," *Journal of
Global Optimization*, **68** (2017), no. 2, pp. 357–366.

A. Rajkumar, S. Ghoshal, L.-H. Lim, and S. Agarwal, "Ranking from stochastic pairwise preferences: recovering
Condorcet winners and tournament solution sets at the top,"
*Proceedings of the 32nd International Conference on Machine
Learning* (ICML), JMLR: W&CP **37** (2015), pp. 665–673.

B. St. Thomas, K. You, L. Lin, L.-H. Lim, and S. Mukherjee, "Learning subspaces of different
dimensions," *Journal of Computational and Graphical Statistics*,
**31** (2022), no. 2, pp. 337–350.

K. Ye and L.-H. Lim, "Schubert
varieties and distances between subspaces of different dimensions,"
*SIAM Journal on Matrix Analysis and Applications*, **37** (2016),
no. 3, pp. 1176–1197.

C.J. Hillar and L.-H. Lim, "Most tensor problems are NP-hard," *Journal of
the ACM*, **60** (2013), no. 6, Art. 45, 39 pp.

L.-H. Lim, "Tensors and hypermatrices," Chapter
15, 30 pp., in L.
Hogben (Ed.), *Handbook of Linear Algebra*, 2nd Ed., CRC Press, Boca
Raton, FL, 2013.

L.-H. Lim and P. Comon, "Blind multilinear identification," *IEEE
Transactions on Information Theory*, **60** (2014), no. 2,
pp. 1260–1280.

K. Ye and
L.-H. Lim, "Every
matrix is a product of Toeplitz matrices," *Foundations of
Computational Mathematics*, **16** (2016), no. 3, pp. 577–598.

D. Gleich and L.-H. Lim, "Rank
aggregation via nuclear norm minimization," *Proceedings of the ACM
SIGKDD Conference on Knowledge Discovery and Data Mining* (KDD '11),
**17** (2011), pp. 60–68.

M. Gu, L.-H. Lim, and C.J. Wu, "PARNES: A rapidly convergent algorithm
for accurate recovery of sparse and approximately sparse signals,"
*Numerical Algorithms*, **64** (2013), no. 2, pp.
321–347.

X. Jiang, L.-H. Lim, Y. Yao, and Y. Ye, "Statistical ranking and combinatorial
Hodge theory," *Mathematical Programming*, Series B: Special
Issue on
Optimization and Machine Learning, **127** (2011), no. 1, pp.
203–244. [AMS Feature Column: "Who's number 1? Hodge theory will tell us"]

T. Schultz, A. Fuster, A. Ghosh, L. Florack,
R. Deriche, and L.-H. Lim, "Higher-order tensors in diffusion imaging," pp.
129–161,
C.-F. Westin et al. (Eds.), *Visualization and Processing of Tensors and
Higher Order Descriptors for Multi-Valued Data*, Springer-Verlag,
Berlin Heidelberg, 2014.

L.-H. Lim and P. Comon, "Multiarray signal processing: tensor decomposition
meets compressed sensing," *Comptes Rendus de l'Académie des
sciences*, Series IIB – Mechanics, **338** (2010), no. 6, pp.
311–320.

B. Savas and L.-H. Lim, "Quasi-Newton methods on Grassmannians and
multilinear approximations of tensors," *SIAM Journal on
Scientific Computing*, **32** (2010), no. 6, pp.
3352–3393.

L.-H. Lim and P. Comon, "Nonnegative
approximations of nonnegative tensors," *Journal of
Chemometrics*, **23** (2009), no. 7–8, pp. 432–441.

M. Mørup, L. Hansen, S. Arnfred, L.-H. Lim, and K. Madsen, "Shift invariant multilinear
decomposition of neuroimaging data," *NeuroImage*,
**42** (2008), no. 4, pp. 1439–1450.

J. Morton and L.-H. Lim, "Principal cumulant component analysis,"
(extended abstract), *preprint*, (2009).

P. Comon, G. Golub, L.-H. Lim, and B. Mourrain,
"Symmetric tensors and symmetric
tensor rank,"
*SIAM Journal on Matrix Analysis and Applications*,
**30** (2008), no. 3, pp. 1254–1279.

V. De Silva and L.-H. Lim,
"Tensor rank and the ill-posedness of
the best low-rank approximation problem,"
*SIAM Journal on Matrix Analysis and Applications*,
**30** (2008), no. 3, pp. 1084–1127.

P. Comon, G. Golub, L.-H. Lim, and B. Mourrain,
"Genericity and rank deficiency of
high order symmetric tensors,"
*Proceedings of the IEEE International Conference on Acoustics, Speech,
and Signal Processing* (ICASSP '06),
**31** (2006), no. 3, pp. 125–128.

L.-H. Lim,
"Singular values and eigenvalues of
tensors: a variational approach,"
*Proceedings of the IEEE International Workshop on Computational
Advances in Multi-Sensor Adaptive Processing* (CAMSAP '05),
**1** (2005), pp. 129–132.

L.-H. Lim, J. Packer, and K. Taylor,
"Direct integral decomposition of the
wavelet representation,"
*Proceedings of the American Mathematical Society*,
**129** (2001), no. 10, pp. 3057–3067.

L.-H. Lim,
"Security of the Cao–Li public
key cryptosystem,"
*Electronics Letters*,
**34** (1998), no. 2, pp. 170–172.

J. Foo, L.-H. Lim, and K. S.-W. Wong, "Discovering latent
macroeconomic effects on peer-to-peer lending," *Journal of
FinTech*,
(2023), to appear.

L.-H. Lim, "Feature interviews:
"The field is as exciting as ever" — interview of Shmuel
Friedland," *IMAGE: Bulletin of the International Linear Algebra
Society*, **59** (2017), Fall, pp. 3–8.

M. Mahoney, L.-H. Lim, and G. Carlsson,
"MMDS 2008: Algorithmic and
statistical challenges in modern large-scale data analysis are the
focus," *Statistical Computing and Graphics*, **20**
(2009), no. 1, pp. 12–18.

M. Mahoney, L.-H. Lim, and G. Carlsson,
"Algorithmic, statistical
challenges in data analysis focus of MMDS 2008," *AMSTAT News*,
**384** (2009), pp. 16–19.

M. Mahoney, L.-H. Lim, and G. Carlsson,
"MMDS 2008: Algorithmic and statistical challenges in modern large-scale
data analysis, Parts I & II,"
*SIAM News*, **42** (2009), no. 1, pp. 8, & no. 2, pp.
8–9. [Chinese translation: "MMDS 2008:
现代大规模数据集分析中的算法和统计方面的挑战,"
*数学译林*, **31** (2012), no. 1, pp.
83–88.]

M. Mahoney, L.-H. Lim, and G. Carlsson,
"Algorithmic and statistical
challenges in modern large-scale data analysis are the focus of MMDS
2008," *KDD Explorations*, **10** (2008), no. 2, pp.
57–60.

M. Mahoney, L.-H. Lim, and G. Carlsson,
"Algorithms for modern
massive data sets," *IMS Bulletin*,
**37** (2008), no. 10, pp. 10–11.

G. Golub, M. Mahoney, P. Drineas, and L.-H. Lim,
"Bridging the gap between numerical
linear algebra, theoretical computer science, and data applications,"
*SIAM News*,
**39** (2006), no. 8, pp. 1 & 16.

God grant that no one else has done

The work I want to do,

Then give me the wit to write it up

In decent English too.

*Applied Optics*, **8** (1969), no. 2, p. 273.

**Contact:** Comments on these pages are welcome. Please write to
lekheng@uchicago.edu.