2 citations · 4 across the 10 of their papers we have counts for
8 papers · 1 filter
Preconditioned Truncated Single-Sample Estimators for Scalable Stochastic Optimization
Tianshi Xu, Difeng Cai, Hua Huang +2
Many large-scale stochastic optimization algorithms involve repeated solutions of linear systems or evaluations of log-determinants. In these regimes, computing exact solutions is…
Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations
Difeng Cai, Paulina Sepúlveda
The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numeric…
Data-Driven Linear Complexity Low-Rank Approximation of General Kernel Matrices: A Geometric Approach
Difeng Cai, Edmond Chow, Yuanzhe Xi
A general, {\em rectangular} kernel matrix may be defined as where is a kernel function and where and are two…
Data-driven Construction of Hierarchical Matrices with Nested Bases
Difeng Cai, Hua Huang, Edmond Chow +1
Hierarchical matrices provide a powerful representation for significantly reducing the computational complexity associated with dense kernel matrices. For general kernel functions,…
Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations
Difeng Cai, Zhiqiang Cai
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an expli…
Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets
Difeng Cai, James Nagy, Yuanzhe Xi
Kernel methods are used frequently in various applications of machine learning. For large-scale high dimensional applications, the success of kernel methods hinges on the ability t…
SMASH: Structured matrix approximation by separation and hierarchy
Difeng Cai, Edmond Chow, Yousef Saad +1
This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel f…
An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane
Difeng Cai
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) i…