55 citations · 214 across the 36 of their papers we have counts for
38 papers
Generalizing Frobenius Inversion to Quaternion Matrices
Qiyuan Chen, J. Uhlmann, Ke Ye
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the…
Lower Bounds of Functions on Finite Abelian Groups
Jiangting Yang, Ke Ye, Lihong Zhi
The problem of computing the optimum of a function on a finite set is an important problem in mathematics and computer science. Many combinatorial problems such as MAX-SAT and MAXC…
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…
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)^…
Sparse sum of Hermitian squares in group algebras of finite groups
Jianting Yang, Ke Ye, Lihong Zhi
Nonnegative elements in group algebras play a central role in harmonic analysis, operator algebras, and computational optimization. This paper investigates sparse sum-of-Hermitian-…
Skew-sparse matrix multiplication
Qiao-Long Huang, Ke Ye, Xiao-Shan Gao
Based on the observation that is isomorphic to a quotient skew polynomial ring, we propose a new method for matrix multiplicat…
When geometry meets optimization theory: partially orthogonal tensors
Ke Ye, Shenglong Hu
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employ…
Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time
Jianting Yang, Ke Ye, Lihong Zhi
The problem of verifying the nonnegativity of a function on a finite abelian group is a long-standing challenging problem. The basic theory of representation theory of finite group…
Simpler Grassmannian optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
There are two widely used models for the Grassmannian , as the set of equivalence classes of orthogonal matrices $\operatorname{O}(n)/(\operatorname{O}(k) \…
Intrinsic Gaussian Processes on Manifolds and Their Accelerations by Symmetry
Ke Ye, Mu Niu, Pokman Cheung +2
Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primari…
Symmetric Tensor Decompositions On Varieties
Jiawang Nie, Ke Ye, Lihong Zhi
This paper discusses the problem of symmetric tensor decomposition on a given variety : decomposing a symmetric tensor into the sum of tensor powers of vectors contained in .…
Linear Convergence of an Alternating Polar Decomposition Method for Low Rank Orthogonal Tensor Approximations
Shenglong Hu, Ke Ye
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating pol…
Optimization on flag manifolds
Ke Ye, Ken Sze-Wai Wong, Lek-Heng Lim
A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE;…
Semi-Riemannian Manifold Optimization
Tingran Gao, Lek-Heng Lim, Ke Ye
We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each…
3d TQFTs from Argyres-Douglas theories
Mykola Dedushenko, Sergei Gukov, Hiraku Nakajima +2
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on with a non-trivi…
The Grassmannian of affine subspaces
Lek-Heng Lim, Ken Sze-Wai Wong, Ke Ye
The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear sub…
Geometric distance between positive definite matrices of different dimensions
Lek-Heng Lim, Rodolphe Sepulchre, Ke Ye
We show how the Riemannian distance on , the cone of real symmetric or complex Hermitian positive definite matrices, may be used to naturally define…
Topology of tensor ranks
Pierre Comon, Lek-Heng Lim, Yang Qi +1
We study path-connectedness and homotopy groups of sets of tensors defined by tensor rank, border rank, multilinear rank, as well as their symmetric counterparts for symmetric tens…
Tensor network ranks
Ke Ye, Lek-Heng Lim
In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-unive…
Argyres-Douglas matter and S-duality: Part II
Dan Xie, Ke Ye
We study S-duality of Argyres-Douglas theories obtained by compactification of 6d (2,0) theories of ADE type on a sphere with irregular punctures. The weakly coupled descriptions a…
On the Chiral Ring and Vacua of Adjoint SQCD
Ke Ye
We analyze classical and quantum chiral ring relations of four dimensional adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the m…
Hankel tensor decompositions and ranks
Jiawang Nie, Ke Ye
Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermon…
Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
Laura Fredrickson, Du Pei, Wenbin Yan +1
We use Coulomb branch indices of Argyres-Douglas theories on to quantize moduli spaces of wild/irregular Hitchin systems. In particular, we obtain…
Numerical algorithms on the affine Grassmannian
Lek-Heng Lim, Ken Sze-Wai Wong, Ke Ye
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points bein…