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A survey of recent developments in parallel implementations of Gaussian elimination

https://doi.org/10.1002/cpe.3306
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/cpe.1301openalex-snapshot
Parallel tiled QR factorization for multicore architectures
inferredcites →https://doi.org/10.1002/cpe.1463openalex-snapshot
Parallelizing dense and banded linear algebra libraries using SMPSs
inferredcites →https://doi.org/10.1002/cpe.1467openalex-snapshot
Scheduling dense linear algebra operations on multicore processors
inferredcites →https://doi.org/10.1002/cpe.1476openalex-snapshot
Complex version of high performance computing LINPACK benchmark (HPL)
inferredcites →https://doi.org/10.1002/cpe.1631openalex-snapshot
StarPU: a unified platform for task scheduling on heterogeneous multicore architectures
inferredcites →https://doi.org/10.1002/cpe.v20:13openalex-snapshot
Parallel tiled QR factorization for multicore architectures
inferredcites →https://doi.org/10.1007/11558958_49openalex-snapshot
Rapid Development of High-Performance Out-of-Core Solvers
inferredcites →https://doi.org/10.1007/978-0-387-35407-1_13openalex-snapshot
New Generalized Matrix Data Structures Lead to a Variety of High-Performance Algorithms
inferredcites →https://doi.org/10.1016/j.compstruc.2006.08.029openalex-snapshot
A FETI-like domain decomposition method for coupling finite elements and boundary elements in large-size problems of acoustic scattering
inferredcites →https://doi.org/10.1016/j.parco.2008.10.002openalex-snapshot
A class of parallel tiled linear algebra algorithms for multicore architectures
inferredcites →https://doi.org/10.1017/s0022112009991972openalex-snapshot
Noise radiation from a ducted rotor in a swirling-translating flow
inferredcites →https://doi.org/10.1088/0029-5515/46/7/s02openalex-snapshot
Global-wave solutions with self-consistent velocity distributions in ion cyclotron heated plasmas
inferredcites →https://doi.org/10.1109/74.80522openalex-snapshot
Origin and development of the method of moments for field computation
inferredcites →https://doi.org/10.1109/aiccsa.2011.6126599openalex-snapshot
LU factorization for accelerator-based systems
inferredcites →https://doi.org/10.1109/clustr.2007.4629221openalex-snapshot
Satisfying your dependencies with SuperMatrix
inferredcites →https://doi.org/10.1109/hpec.2012.6408679openalex-snapshot
Anatomy of a globally recursive embedded LINPACK benchmark
inferredcites →https://doi.org/10.1109/ipdps.2010.5470348openalex-snapshot
Adapting communication-avoiding LU and QR factorizations to multicore architectures
inferredcites →https://doi.org/10.1109/ipdps.2011.91openalex-snapshot
Two-Stage Tridiagonal Reduction for Dense Symmetric Matrices Using Tile Algorithms on Multicore Architectures
inferredcites →https://doi.org/10.1109/ipdps.2012.13openalex-snapshot
A Comprehensive Study of Task Coalescing for Selecting Parallelism Granularity in a Two-Stage Bidiagonal Reduction
inferredcites →https://doi.org/10.1109/map.2008.4653660openalex-snapshot
Solving large complex problems using a higher-order basis: parallel in-core and out-of-core integral-equation solvers
inferredcites →https://doi.org/10.1109/pdp.2010.67openalex-snapshot
hwloc: A Generic Framework for Managing Hardware Affinities in HPC Applications
inferredcites →https://doi.org/10.1109/sc.2008.5214287openalex-snapshot
Communication Avoiding Gaussian elimination
inferredcites →https://doi.org/10.1109/tc.1985.1676570openalex-snapshot
Analysis of Pairwise Pivoting in Gaussian Elimination
inferredcites →https://doi.org/10.1109/tpds.2009.79openalex-snapshot
Parallel Two-Sided Matrix Reduction to Band Bidiagonal Form on Multicore Architectures
inferredcites →https://doi.org/10.1137/0611023openalex-snapshot
Average-Case Stability of Gaussian Elimination
inferredcites →https://doi.org/10.1137/1.9781611971446openalex-snapshot
Applied Numerical Linear Algebra
inferredcites →https://doi.org/10.1137/100788926openalex-snapshot
CALU: A Communication Optimal LU Factorization Algorithm
inferredcites →https://doi.org/10.1137/120863691openalex-snapshot
LU Factorization with Panel Rank Revealing Pivoting and Its Communication Avoiding Version
inferredcites →https://doi.org/10.1137/s0895479895291741openalex-snapshot
Probabilistic Analysis of Gaussian Elimination Without Pivoting
inferredcites →https://doi.org/10.1145/1527286.1527288openalex-snapshot
Programming matrix algorithms-by-blocks for thread-level parallelism
inferredcites →https://doi.org/10.1145/1654059.1654080openalex-snapshot
Comparative study of one-sided factorizations with multiple software packages on multi-core hardware
inferredcites →https://doi.org/10.1145/1693453.1693484openalex-snapshot
Scaling LAPACK panel operations using parallel cache assignment
inferredcites →https://doi.org/10.1145/2063384.2063394openalex-snapshot
Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels
inferredcites →https://doi.org/10.1145/2132876.2132885openalex-snapshot
High performance matrix inversion based on LU factorization for multicore architectures
inferredcites →https://doi.org/10.1145/2168773.2168775openalex-snapshot
Parallel and Cache-Efficient In-Place Matrix Storage Format Conversion
inferredcites →https://doi.org/10.1145/2427023.2427025openalex-snapshot
Accelerating Linear System Solutions Using Randomization Techniques
inferredcites →https://doi.org/10.1145/321075.321076openalex-snapshot
Error Analysis of Direct Methods of Matrix Inversion
inferredcites →https://doi.org/10.1146/annurev.fl.22.010190.001351openalex-snapshot
Panel Methods In Computational Fluid Dynamics
inferredcites →https://doi.org/10.1147/rd.416.0737openalex-snapshot
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
inferredcites →https://doi.org/10.1155/2001/569670openalex-snapshot
Recursive Approach in Sparse Matrix LU Factorization
inferredcites →https://doi.org/10.1177/109434209300700203openalex-snapshot
Large Dense Numerical Linear Algebra in 1993: the Parallel Computing Influence
inferredcites →https://doi.org/10.2307/2003558openalex-snapshot
The Algebraic Eigenvalue Problem
inferredcites →https://doi.org/10.3233/978-1-61499-041-3-429openalex-snapshot
Exploiting Fine-Grain Parallelism in Recursive LU Factorization
inferredcites →https://doi.org/10.48550/arxiv.0809.2407openalex-snapshot
Implementing Communication-Optimal Parallel and Sequential QR Factorizations
inferredcites →https://doi.org/10.5555/1413370.1413400openalex-snapshot
Communication avoiding Gaussian elimination
inferredcites →https://doi.org/10.5860/choice.35-3919openalex-snapshot
Applied numerical linear algebra

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Performance Analysis of Direct Gaussian Solvers for Solving 2D Elastodynamic Problem of a Finite-Sized Solid Containing Cavities on CPUs and MICs
inferred← citeshttps://doi.org/10.1007/978-3-319-31323-8_19openalex-snapshot
Parallelized Solution of Banded Linear Systems with an Introduction to p-adic Computation
inferred← citeshttps://doi.org/10.1007/978-3-319-97277-0_30openalex-snapshot
Performance Analysis of Intel Xeon Phi MICs and Intel Xeon CPUs for Solving Dense Systems of Linear Algebraic Equations: Case Study of Boundary Element Method for Flow Around Airfoils
inferred← citeshttps://doi.org/10.1007/s10766-016-0441-6openalex-snapshot
Porting the PLASMA Numerical Library to the OpenMP Standard
inferred← citeshttps://doi.org/10.1007/s11075-016-0251-3openalex-snapshot
An asynchronous direct solver for banded linear systems
inferred← citeshttps://doi.org/10.1016/j.future.2024.06.004openalex-snapshot
Batched sparse and mixed-precision linear algebra interface for efficient use of GPU hardware accelerators in scientific applications
inferred← citeshttps://doi.org/10.1016/j.ifacol.2017.08.2026openalex-snapshot
Hardware Tailored Linear Algebra for Implicit Integrators in Embedded NMPC
inferred← citeshttps://doi.org/10.1016/j.jalgebra.2025.11.009openalex-snapshot
A parallel algorithm for Gaussian elimination over finite fields
inferred← citeshttps://doi.org/10.1016/j.laa.2017.04.007openalex-snapshot
Numerically safe Gaussian elimination with no pivoting
inferred← citeshttps://doi.org/10.1109/access.2019.2951746openalex-snapshot
Progressive Multicore RLNC Decoding With Online DAG Scheduling
inferred← citeshttps://doi.org/10.1109/csci62032.2023.00180openalex-snapshot
Accelerated Gauss-Huard Algorithm on Hybrid GPU-CPU: Look-Ahead with the Delayed Algorithm Approach
inferred← citeshttps://doi.org/10.1109/dcis67520.2025.11281919openalex-snapshot
Configurable Ultra-High-Throughput QRD FPGA Accelerators for Small Matrices
inferred← citeshttps://doi.org/10.1109/icpads60453.2023.00253openalex-snapshot
Characterize and Optimize Dense Linear Solver on Multi-core CPUs
inferred← citeshttps://doi.org/10.1109/ijcnn.2017.7966328openalex-snapshot
A mixture of multiple linear classifiers with sample weight and manifold regularization
inferred← citeshttps://doi.org/10.1109/ipdps64566.2025.00094openalex-snapshot
Scalable and Portable LU Factorization with Partial Pivoting on Top of Runtime Systems
inferred← citeshttps://doi.org/10.1109/scala51936.2020.00010openalex-snapshot
Replacing Pivoting in Distributed Gaussian Elimination with Randomized Techniques
inferred← citeshttps://doi.org/10.1109/siet48054.2019.8985999openalex-snapshot
Comparative Study of Numerical Methods in Multiple Linear Regression For Stock Prediction Jakarta Islamic Index (JII)
inferred← citeshttps://doi.org/10.1109/srds47363.2019.00022openalex-snapshot
Fault Tolerant High Performance Solver for Linear Equation Systems
inferred← citeshttps://doi.org/10.1109/srds51746.2020.00034openalex-snapshot
Solving Linear Systems on High Performance Hardware with Resilience to Multiple Hard Faults
inferred← citeshttps://doi.org/10.1109/synasc.2016.069openalex-snapshot
A Hybrid CPU/GPU Approach for the Parallel Algebraic Recursive Multilevel Solver pARMS
inferred← citeshttps://doi.org/10.1109/tpds.2018.2808964openalex-snapshot
Symmetric Indefinite Linear Solver Using OpenMP Task on Multicore Architectures
inferred← citeshttps://doi.org/10.1145/3264491openalex-snapshot
PLASMA
inferred← citeshttps://doi.org/10.1145/3332466.3374538openalex-snapshot
Using sample-based time series data for automated diagnosis of scalability losses in parallel programs
inferred← citeshttps://doi.org/10.1145/3577193.3593731openalex-snapshot
Using Additive Modifications in LU Factorization Instead of Pivoting
inferred← citeshttps://doi.org/10.1145/3649153.3649210openalex-snapshot
QR-PULP: Streamlining QR Decomposition for RISC-V Parallel Ultra-Low-Power Platforms
inferred← citeshttps://doi.org/10.1145/3699714openalex-snapshot
Generalizing Random Butterfly Transforms to Arbitrary Matrix Sizes
inferred← citeshttps://doi.org/10.15439/2015f177openalex-snapshot
Using Random Butterfly Transformations in Parallel Schur Complement-Based Preconditioning
inferred← citeshttps://doi.org/10.15439/2022f251openalex-snapshot
Influence of loop transformations on performance and energy consumption of the multithreded WZ factorization
inferred← citeshttps://doi.org/10.15439/2023f6213openalex-snapshot
Impact of processor frequency scaling on performance and energy consumption for WZ factorization on multicore architecture
inferred← citeshttps://doi.org/10.2478/amcs-2019-0030openalex-snapshot
The Parallel Tiled WZ Factorization Algorithm for Multicore Architectures
inferred← citeshttps://doi.org/10.31390/gradschool_dissertations.4486openalex-snapshot
Maintaining High Performance Across All Problem Sizes and Parallel Scales Using Microkernel-based Linear Algebra
inferred← citeshttps://doi.org/10.70675/42fab030zaf8ez47cbzaa74ze8aacaa9883eopenalex-snapshot
Programmation des architectures hétérogènes à l'aide de tâches divisibles ou modulables
inferred← citeshttps://doi.org/10.70675/d568f732zf598z481aza8fcz023fecb8cd1copenalex-snapshot
A parallel iterative solver for large sparse linear systems enhanced with randomization and GPU accelerator, and its resilience to soft errors
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