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A Nondeterministic Parallel Algorithm for General Unsymmetric Sparse LU Factorization

https://doi.org/10.1137/0611028
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Y12M
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Parallel sparse Gaussian elimination with partial pivoting
inferredcites →https://doi.org/10.1016/0005-1098(90)90146-9openalex-snapshot
Direct methods for sparse matrices
inferredcites →https://doi.org/10.1016/0167-8191(86)90014-1openalex-snapshot
Computational models and task scheduling for parallel sparse Cholesky factorization
inferredcites →https://doi.org/10.1016/0167-8191(86)90019-0openalex-snapshot
Parallel implementation of multifrontal schemes
inferredcites →https://doi.org/10.1016/0167-8191(89)90016-1openalex-snapshot
Independent set orderings for parallel matrix factorization by Gaussian elimination
inferredcites →https://doi.org/10.1016/0377-0427(89)90368-3openalex-snapshot
Multiprocessing a sparse matrix code on the Alliant FX/8
inferredcites →https://doi.org/10.1016/b978-1-4832-3187-7.50018-0openalex-snapshot
A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS
inferredcites →https://doi.org/10.1093/imamat/10.1.118openalex-snapshot
On the Automatic Scaling of Matrices for Gaussian Elimination
inferredcites →https://doi.org/10.1109/12.42123openalex-snapshot
Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor
inferredcites →https://doi.org/10.1109/12.9742openalex-snapshot
Pairwise reduction for the direct, parallel solution of sparse, unsymmetric sets of linear equations
inferredcites →https://doi.org/10.1109/proc.1967.6011openalex-snapshot
Direct solutions of sparse network equations by optimally ordered triangular factorization
inferredcites →https://doi.org/10.1109/tc.1980.1675634openalex-snapshot
A Computation Model of Parallel Solution of Linear Equations
inferredcites →https://doi.org/10.1109/tc.1982.1675979openalex-snapshot
A Data Structure for Parallel L/U Decomposition
inferredcites →https://doi.org/10.1126/science.231.4741.967openalex-snapshot
Parallel Supercomputing Today and the Cedar Approach
inferredcites →https://doi.org/10.1137/0134014openalex-snapshot
Algorithmic Aspects of Vertex Elimination on Directed Graphs
inferredcites →https://doi.org/10.1137/0602010openalex-snapshot
Computing the Minimum Fill-In is NP-Complete
inferredcites →https://doi.org/10.1137/0717003openalex-snapshot
On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique
inferredcites →https://doi.org/10.1137/0717024openalex-snapshot
A Minimal Storage Implementation of the Minimum Degree Algorithm
inferredcites →https://doi.org/10.1137/0905045openalex-snapshot
The Multifrontal Solution of Unsymmetric Sets of Linear Equations
inferredcites →https://doi.org/10.1137/0906028openalex-snapshot
An Implementation of Gaussian Elimination with Partial Pivoting for Sparse Systems
inferredcites →https://doi.org/10.1137/0909008openalex-snapshot
A Data Structure for Sparse $QR$ and $LU$ Factorizations
inferredcites →https://doi.org/10.1137/0909029openalex-snapshot
Equivalent Sparse Matrix Reordering by Elimination Tree Rotations
inferredcites →https://doi.org/10.1137/0909058openalex-snapshot
Sparse Partial Pivoting in Time Proportional to Arithmetic Operations
inferredcites →https://doi.org/10.1145/214392.214398openalex-snapshot
Modification of the minimum-degree algorithm by multiple elimination
inferredcites →https://doi.org/10.1145/355815.355817openalex-snapshot
Some Design Features of a Sparse Matrix Code
inferredcites →https://doi.org/10.1145/356044.356047openalex-snapshot
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
inferredcites →https://doi.org/10.1145/62038.62043openalex-snapshot
Sparse matrix test problems
inferredcites →https://doi.org/10.1177/109434208900300303openalex-snapshot
Vectorization of a Multiprocessor Multifrontal Code
inferredcites →https://doi.org/10.2307/2007640openalex-snapshot
Computer Solution of Large Sparse Positive Definite Systems.

What points at this work

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

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Sparse Matrix Computations on the Hypercube and Related Networks
inferred← citeshttps://doi.org/10.1007/11666806_5openalex-snapshot
Parallel Treatment of General Sparse Matrices
inferred← citeshttps://doi.org/10.1007/3-540-49164-3_4openalex-snapshot
Parallel Pivots LU Algorithm on the Cray T3E
inferred← citeshttps://doi.org/10.1007/978-3-642-21913-9_4openalex-snapshot
Biophysical and Biochemical Determinants of Contractile Force Generation, Regulation and Function
inferred← citeshttps://doi.org/10.1007/978-3-642-76717-3_13openalex-snapshot
Parallel Algorithms for General Sparse Systems
inferred← citeshttps://doi.org/10.1007/bf02238079openalex-snapshot
A locally optimized reordering algorithm and its application to a parallel sparse linear system solver
inferred← citeshttps://doi.org/10.1007/bf02577871openalex-snapshot
Parallel-access memory management using fast-fits
inferred← citeshttps://doi.org/10.1007/bfb0030181openalex-snapshot
PARASPAR: Parallel solvers for sparse linear algebraic systems
inferred← citeshttps://doi.org/10.1007/bfb0046701openalex-snapshot
Sparse LU factorization of the Cray T3D
inferred← citeshttps://doi.org/10.1016/0743-7315(92)90066-vopenalex-snapshot
Parallel structured networks for solving a wide variety of matrix algebra problems
inferred← citeshttps://doi.org/10.1016/s0167-8191(96)00047-6openalex-snapshot
Solving large nonsymmetric sparse linear systems using MCSPARSE
inferred← citeshttps://doi.org/10.1016/s0167-8191(99)00077-0openalex-snapshot
Developments and trends in the parallel solution of linear systems
inferred← citeshttps://doi.org/10.1016/s0168-2024(99)80012-5openalex-snapshot
References
inferred← citeshttps://doi.org/10.1016/s0377-0427(00)00401-5openalex-snapshot
The impact of high-performance computing in the solution of linear systems: trends and problems
inferred← citeshttps://doi.org/10.1016/s1570-579x(06)80021-2openalex-snapshot
Efficient organization of the matrix computations
inferred← citeshttps://doi.org/10.1016/s1570-579x(06)80028-5openalex-snapshot
Bibliography
inferred← citeshttps://doi.org/10.1016/s1570-8659(00)07002-2openalex-snapshot
Gaussian elimination for the solution of linear systems of equations
inferred← citeshttps://doi.org/10.1017/s0962492916000076openalex-snapshot
A survey of direct methods for sparse linear systems
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.001.0001openalex-snapshot
Direct Methods for Sparse Matrices
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0001openalex-snapshot
Glossary of Symbols
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0005openalex-snapshot
Copyright Page
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.002.0006openalex-snapshot
Preface
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0001openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0002openalex-snapshot
Sparse matrices: storage schemes and simple operations
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0003openalex-snapshot
Gaussian elimination for dense matrices: the algebraic problem
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0004openalex-snapshot
Gaussian elimination for dense matrices: numerical considerations
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0005openalex-snapshot
Gaussian elimination for sparse matrices: an introduction
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0006openalex-snapshot
Reduction to block triangular form
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0007openalex-snapshot
Local pivotal strategies for sparse matrices
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0008openalex-snapshot
Ordering sparse matrices for band solution
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0009openalex-snapshot
Orderings based on dissection
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0010openalex-snapshot
Implementing Gaussian elimination without symbolic factorize
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0011openalex-snapshot
Implementing Gaussian elimination with symbolic factorize
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Gaussian elimination using trees
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Graphs for symmetric and unsymmetric matrices
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The solve phase
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Other sparsity-oriented issues
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Matrix and vector norms
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Pictures of sparse matrices
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Solutions to selected exercises
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Sparse Numerical Linear Algebra: Direct Methods and Preconditioning
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Space efficient parallel buddy memory management
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A Concurrent Dynamic Task Graph
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Parallel Sparse LU Decomposition on a Mesh Network of Transputers
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Parallel Algorithms for Sparse Linear Systems
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Design and Implementation of a Parallel Markowitz Threshold Algorithm
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An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
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Algorithm 1037: SuiteSparse:GraphBLAS: Parallel Graph Algorithms in the Language of Sparse Linear Algebra
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Parallelizing the Dual Simplex Method
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Efficient Procedure Improving Precision of High Conditioned Matrices in Electronic Circuits Analysis
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