59 citations · 93 across the 17 of their papers we have counts for
19 papers
A Note on Eigenvalues of Perturbed Hermitian Matrices
Chi-Kwong Li, Ren-Cang Li
Let $$ A=\left(\begin{array}{cc} H_1 & E^*\\ E & H_2\end{array}\right) \quad \hbox{ and } \quad \wtd A=\left(\begin{array}{cc} H_1 & O\\ O & H_2\end{array}\right)$$ be two -by-$…
A Theory of the NEPv Approach for Optimization On the Stiefel Manifold
Ren-Cang Li
The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first ord…
Variations of Orthonormal Basis Matrices of Subspaces
Zhongming Teng, Ren-Cang Li
An orthonormal basis matrix of a subspace is known not to be unique, unless there are some kinds of normalization requirements. One of them is to require that $X^{\r…
On Generalizing Trace Minimization Principles, II
Xin Liang, Ren-Cang Li
This paper is concerned with establishing a trace minimization principle for two Hermitian matrix pairs. Specifically, we will answer the question: when is $\inf_X\operatorname{tr}…
Locally Unitarily Invariantizable NEPv and Convergence Analysis of SCF
Ding Lu, Ren-Cang Li
We consider a class of eigenvector-dependent nonlinear eigenvalue problems (NEPv) without the unitary invariance property. Those NEPv commonly arise as the first-order optimality c…
A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis
Dong Min Roh, Zhaojun Bai, Ren-Cang Li
Much like the classical Fisher linear discriminant analysis (LDA), the recently proposed Wasserstein discriminant analysis (WDA) is a linear dimensionality reduction method that se…