17 citations · 57 across the 11 of their papers we have counts for
12 papers
Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning
James E. Garrison, Chao Chen, Ilse C. F. Ipsen
Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numer…
Solving Linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations
Chao Chen, Per-Gunnar Martinsson
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathemat…
Discovering Governing Equations by Machine Learning implemented with Invariance
Chao Chen, Xiaowei Jin, Hui Li
The partial differential equation (PDE) plays a significantly important role in many fields of science and engineering. The conventional case of the derivation of PDE mainly relies…
Overlapping Domain Decomposition Preconditioner for Integral Equations
Chao Chen, George Biros
The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coeff…
RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems
Chao Chen, Tianyu Liang, George Biros
We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspecti…
Fast Approximation of the Gauss-Newton Hessian Matrix for the Multilayer Perceptron
Chao Chen, Severin Reiz, Chenhan Yu +2
We introduce a fast algorithm for entry-wise evaluation of the Gauss-Newton Hessian (GNH) matrix for the fully-connected feed-forward neural network. The algorithm has a precomputa…