107 citations · 551 across the 65 of their papers we have counts for
9 papers · 1 filter
Simpler flag optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, me…
Haagerup bound for quaternionic Grothendieck inequality
Shmuel Friedland, Zehua Lai, Lek-Heng Lim
We present here several versions of the Grothendieck inequality over the skew field of quaternions: The first one is the standard Grothendieck inequality for rectangular matrices,…
Stochastic Steffensen method
Minda Zhao, Zehua Lai, Lek-Heng Lim
Is it possible for a first-order method, i.e., only first derivatives allowed, to be quadratically convergent? For univariate loss functions, the answer is yes -- the Steffensen me…
LU decomposition and Toeplitz decomposition of a neural network
Yucong Liu, Simiao Jiao, Lek-Heng Lim
It is well-known that any matrix has an LU decomposition. Less well-known is the fact that it has a 'Toeplitz decomposition' where 's are Toeplitz…
Generalized matrix nearness problems
Zihao Li, Lek-Heng Lim
We show that the global minimum solution of can be found in closed-form with singular value decompositions and generalized singular value decompositions for…
Complex matrix inversion via real matrix inversions
Zhen Dai, Lek-Heng Lim, Ke Ye
We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^…