Chao Chen
Numerical linear algebra, High-performance computing, Numerical analysis, Parallel computing, Randomized algorithms, Data science
Works (25)
Updated: April 4th, 2024 09:21
2023 journal article
Efficient algorithms for computing rank‐revealing factorizations on a GPU
Numerical Linear Algebra with Applications, 30(6), e2515.
TL;DR:
Two alternative algorithms for computing a rank‐revealing factorization of the form A=UTV, which use randomized projection techniques to cast most of the flops in terms of matrix‐matrix multiplication, which is exceptionally efficient on the GPU are presented.
(via Semantic Scholar)
arxiv.org (repository)
Sources: Crossref, NC State University Libraries, ORCID
Added: January 28, 2024
2022 journal article
Overlapping Domain Decomposition Preconditioner for Integral Equations
SIAM Journal on Scientific Computing, 44(6), A3617–A3644.
TL;DR:
This work introduces a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with existing fast direct solvers and applies the recursive skeletonization to subproblems associated with every subdomain.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2022 conference paper
Solving Linear Systems on a GPU with Hierarchically Off-Diagonal Low-Rank Approximations
SC22: International Conference for High Performance Computing, Networking, Storage and Analysis, 1–15.
Event: SC22: International Conference for High Performance Computing, Networking, Storage and Analysis
TL;DR:
Algorithms for factorizing HODLR matrices and for applying the factorizations on a GPU leverage the efficiency of batched dense linear algebra, and they scale nearly linearly with the matrix size when the numerical ranks are fixed.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2021 journal article
Fast Approximation of the Gauss--Newton Hessian Matrix for the Multilayer Perceptron
SIAM Journal on Matrix Analysis and Applications, 42(1), 165–184.
TL;DR:
A fast algorithm for entry-wise evaluation of the Gauss-Newton Hessian (GNH) matrix for the fully-connected feed-forward neural network and the H-matrix approximation of the GNH matrix for solving linear systems and eigenvalue problems is introduced.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2021 journal article
PBBFMM3D: A parallel black-box algorithm for kernel matrix-vector multiplication
Journal of Parallel and Distributed Computing, 154, 64–73.
TL;DR:
A parallel black-box method for computing kernel matrix-vector multiplication, where the underlying kernel is a non-oscillatory function in three dimensions, which reduces the cost to $O(N)$ work.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2021 journal article
RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems
SIAM Journal on Scientific Computing, 43(6), C411–C438.
TL;DR:
A randomized algorithm, namely {\tt rchol], is introduced to construct an approximate Cholesky factorization for a given sparse Laplacian matrix and is proved to be breakdown free and applied to solving linear systems with symmetric diagonally-dominant matrices.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2020 conference paper
A preconditioner based on sparsified nested dissection and low-rank approximation
XXI Householder Symposium on Numerical Linear Algebra, 128.
Source: ORCID
Added: November 1, 2023
2020 journal article
An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations
SIAM Journal on Matrix Analysis and Applications, 41(2), 715–746.
TL;DR:
This work proposes a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection, based on nested dissection, sparsification and low-rank compression and demonstrates that a version using orthogonal factorization and block-diagonal scaling takes less CG iterations to converge than previous similar algorithms on various kinds of problems.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2020 journal article
Parallelization of the inverse fast multipole method with an application to boundary element method
Computer Physics Communications, 247, 106975.
TL;DR:
An algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems, based on a greedy coloring algorithm, which proved that when σ ≥ 6 , the workload associated with one color is embarrassingly parallel.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2020 report
Scalable spatio-temporal modeling using a fast multipole method for 3D tracer concentration breakthrough data with magnetic resonance imaging.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2019 journal article
A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling
Journal of Computational Physics, 396, 819–836.
TL;DR:
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel, based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the approximation error and significantly improves efficiency.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2019 conference paper
H-matrix approximation of the Gauss-Newton Hessian matrix for the multilayer perceptron
33rd Conference on Neural Information Processing Systems (NeurIPS 2019).
Source: ORCID
Added: November 1, 2023
2019 report
SpaND: An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Sandia ….
Source: ORCID
Added: November 1, 2023
2018 report
A Hierarchical Low-Rank Solver for Sparse Linear Systems and Its Variations.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2018 journal article
A distributed-memory hierarchical solver for general sparse linear systems
Parallel Computing, 74, 49–64.
TL;DR:
A parallel hierarchical solver for general sparse linear systems on distributed-memory machines is presented, which is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2018 report
A hierarchical solver for extruded meshes with applications to ice sheet modeling
In A. D. Baczewski & M. L. Parks (Eds.), Center for Computing Research Summer Proceedings 2017 (Technical Report No. SAND2018-2780O; pp. 3–18). Sandia National Laboratories.
Ed(s): A. Baczewski & M. Parks
Source: NC State University Libraries
Added: November 8, 2023
2018 journal article
A hierarchical solver for extruded meshes with applications to ice sheet modeling
Center for Computing Research Summer Proceedings 2017, (SAND2018-2780O), 3–18.
Ed(s): A. Baczewski & M. Parks
Source: ORCID
Added: February 1, 2024
2018 journal article
Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media
Modelling and Simulation in Materials Science and Engineering, 26(4), 045007.
TL;DR:
This work implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), onebased on the spherical harmonics expansion (Spherical FMM%), one kernel-independent method based onThe Chebyshev interpolation (ChebysheV FMM, and a new kernel- independent method that is designed to be a memory-efficient black-box method that the authors call the Lagrange FMM.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2018 thesis
Parallel Hierarchical Linear Solvers and Fast Multipole Methods with Applications
Stanford University.
Source: ORCID
Added: November 1, 2023
2018 report
Scheduling Parallel Tasks using Graph Coloring.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2017 report
A Hierarchical Low-Rank Solver for Large Sparse Linear Systems.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2017 report
A Parallel Hierarchical Low-Rank Solver for General Sparse Matrices.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2017 report
Hierarchical Matrices and Low-Rank Methods for Extreme-Scale Solvers.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Sandia ….
Source: ORCID
Added: November 1, 2023
2016 journal article
Parallel hierarchical solver for elliptic partial differential equations
CCR, 3.
Source: ORCID
Added: November 1, 2023
2016 conference paper
The Inverse Fast Multipole Method as an Efficient Preconditioner for Dense Linear Systems
Conference on Parallel Processing for Scientific Computing, Date: 2016/04/12-2016/04/15, Location: Paris, France.
Source: ORCID
Added: November 1, 2023
Employment
Updated: September 1st, 2023 22:29
2023 - present
North Carolina State University Raleigh, North Carolina, US
Assistant Professor
Mathematics
Education
Updated: September 1st, 2023 22:35
2014 - 2018
Stanford University Stanford, California, US
PhD
Institute for Computational and Mathematical Engineering
2012 - 2014
Stanford University Stanford, California, US
MS
Institute for Computational and Mathematical Engineering
2008 - 2012
Nankai University Tianjin, CN
BS
Mathematics
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