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A locally optimized reordering algorithm and its application to a parallel sparse linear system solver

https://doi.org/10.1007/bf02238079
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What this work says

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

inferredcites →https://doi.org/10.1007/978-1-4613-8369-7_7openalex-snapshot
Highly Parallel Sparse Triangular Solution
inferredcites →https://doi.org/10.1007/978-1-4615-8675-3_6openalex-snapshot
The Partitioned Preassigned Pivot Procedure (P4)
inferredcites →https://doi.org/10.1007/978-94-017-1116-6openalex-snapshot
Computational Methods for General Sparse Matrices
inferredcites →https://doi.org/10.1007/bf01584086openalex-snapshot
Reinversion with the preassigned pivot procedure
inferredcites →https://doi.org/10.1016/0024-3795(84)90022-3openalex-snapshot
Row-ordering schemes for sparse givens transformations. I. bipartite graph model
inferredcites →https://doi.org/10.1016/0956-0521(90)90006-7openalex-snapshot
A parallel hybrid sparse linear system solver
inferredcites →https://doi.org/10.1038/scientificamerican0984-60openalex-snapshot
Data Structures and Algorithms
inferredcites →https://doi.org/10.1093/acprof:oso/9780198508380.001.0001openalex-snapshot
Direct Methods for Sparse Matrices
inferredcites →https://doi.org/10.1137/0611028openalex-snapshot
A Nondeterministic Parallel Algorithm for General Unsymmetric Sparse LU Factorization
inferredcites →https://doi.org/10.1137/0614059openalex-snapshot
Parallel Sparse LU Decomposition on a Mesh Network of Transputers
inferredcites →https://doi.org/10.1137/0719024openalex-snapshot
Use of Iterative Refinement in the Solution of Sparse Linear Systems
inferredcites →https://doi.org/10.1137/0720023openalex-snapshot
Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
inferredcites →https://doi.org/10.1137/0722022openalex-snapshot
A Structurally Stable Modification of Hellerman–Rarick’s ${\text{P}}^4 $ Algorithm for Reordering Unsymmetric Sparse Matrices
inferredcites →https://doi.org/10.1137/0907080openalex-snapshot
Condition Number Estimators in a Sparse Matrix Software
inferredcites →https://doi.org/10.1137/0908086openalex-snapshot
The Use of BLAS3 in Linear Algebra on a Parallel Processor with a Hierarchical Memory
inferredcites →https://doi.org/10.1137/0911053openalex-snapshot
Use of the ${\text{P}}^4 $ and ${\text{P}}^5 $ Algorithms for In-Core Factorization of Sparse Matrices
inferredcites →https://doi.org/10.1137/1.9781611976137openalex-snapshot
Proceedings of the 2020 SIAM Conference on Parallel Processing for Scientific Computing (PP)
inferredcites →https://doi.org/10.1137/1.9781611977141openalex-snapshot
Proceedings of the 2022 SIAM Conference on Parallel Processing for Scientific Computing (PP)
inferredcites →https://doi.org/10.1137/1032002openalex-snapshot
Parallel Algorithms for Dense Linear Algebra Computations
inferredcites →https://doi.org/10.1142/9789812791245openalex-snapshot
Data Structures and Algorithms
inferredcites →https://doi.org/10.1145/255129.255149openalex-snapshot
Solving general sparse linear systems using conjugate gradient-type methods
inferredcites →https://doi.org/10.1145/62038.62043openalex-snapshot
Sparse matrix test problems
inferredcites →https://doi.org/10.2118/5729-msopenalex-snapshot
Orthomin, an Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations
inferredcites →https://doi.org/10.2172/5604546openalex-snapshot
LAPACK users' guide: Release 1. 0
inferredcites →https://doi.org/10.2307/2007640openalex-snapshot
Computer Solution of Large Sparse Positive Definite Systems.
inferredcites →https://doi.org/10.2307/2008670openalex-snapshot
Direct Methods for Sparse Matrices.
inferredcites →https://doi.org/10.2307/2008751openalex-snapshot
Parallel Processing for Scientific Computing.

What points at this work

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

inferred← citeshttps://doi.org/10.1007/3-540-48158-3_35openalex-snapshot
Parallel Monte Carlo Algorithms for Sparse SLAE Using MPI
inferred← citeshttps://doi.org/10.1007/3-540-60902-4_49openalex-snapshot
A parallel sparse QR-factorization algorithm
inferred← citeshttps://doi.org/10.1007/3-540-62095-8_60openalex-snapshot
Parallel solution of sparse problems by using a sequence of large dense blocks
inferred← citeshttps://doi.org/10.1007/3-540-62598-4_114openalex-snapshot
Using dense matrix computations in the solution of sparse problems
inferred← citeshttps://doi.org/10.1007/978-3-540-24588-9_5openalex-snapshot
Parallel Solution of Very Large Sparse Systems of Linear Algebraic Equations
inferred← citeshttps://doi.org/10.1007/bf02510239openalex-snapshot
Solving sparse linear least-squares problems on some supercomputers by using large dense blocks
inferred← citeshttps://doi.org/10.1007/bfb0030157openalex-snapshot
Two enhancements in a partitioned sparse code
inferred← citeshttps://doi.org/10.1007/bfb0030181openalex-snapshot
PARASPAR: Parallel solvers for sparse linear algebraic systems
inferred← citeshttps://doi.org/10.1016/0898-1221(95)00175-xopenalex-snapshot
Improving the numerical stability and the performance of a parallel sparse solver
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(98)00034-9openalex-snapshot
A coarse-grained parallel QR-factorization algorithm for sparse least squares 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/10.1017/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
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0012openalex-snapshot
Gaussian elimination using trees
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0013openalex-snapshot
Graphs for symmetric and unsymmetric matrices
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0014openalex-snapshot
The solve phase
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.003.0015openalex-snapshot
Other sparsity-oriented issues
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0001openalex-snapshot
Matrix and vector norms
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0002openalex-snapshot
Pictures of sparse matrices
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0003openalex-snapshot
Solutions to selected exercises
inferred← citeshttps://doi.org/10.1137/19m1245815openalex-snapshot
Design and Implementation of a Parallel Markowitz Threshold Algorithm
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