4 citations · 6 across the 6 of their papers we have counts for
6 papers
Accuracy Analysis of the Proxy Point Method with Applications to Some Toeplitz Matrices
Mikhail Lepilov, Jianlin Xia
For some kernel matrices, low-rank approximations can be quickly obtained via analytic techniques. One important class of analytic methods that has received attention in recent yea…
A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network
Zhiqiang Cai, Tong Ding, Min Liu +2
In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advanta…
Making the Nyström method highly accurate for low-rank approximations
Jianlin Xia
The Nyström method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to a…
SuperDC: Stable superfast divide-and-conquer eigenvalue decomposition
Xiaofeng Ou, Jianlin Xia
For dense Hermitian matrices with small off-diagonal (numerical) ranks and in a hierarchically semiseparable form, we give a stable divide-and-conquer eigendecomposition method wit…
Robust and effective eSIF preconditioning for general SPD matrices
Jianlin Xia
We propose an unconditionally robust and highly effective preconditioner for general symmetric positive definite (SPD) matrices based on structured incomplete factorization (SIF),…
Analytical low-rank compression via proxy point selection
Xin Ye, Jianlin Xia, Lexing Ying
It has been known in potential theory that, for some kernels matrices corresponding to well-separated point sets, fast analytical low-rank approximation can be achieved via the use…