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Task scheduling for parallel sparse Cholesky factorization

https://doi.org/10.1007/bf01407861
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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/bf01388998openalex-snapshot
A parallel graph partitioning algorithm for a message-passing multiprocessor
inferredcites →https://doi.org/10.1007/bf01407878openalex-snapshot
Solution of sparse positive definite systems on a shared-memory multiprocessor
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)90064-1openalex-snapshot
Reordering sparse matrices for parallel elimination
inferredcites →https://doi.org/10.1016/0167-8191(89)90101-4openalex-snapshot
Communication results for parallel sparse Cholesky factorization on a hypercube
inferredcites →https://doi.org/10.1016/0377-0427(89)90364-6openalex-snapshot
Solution of sparse positive definite systems on a hypercube
inferredcites →https://doi.org/10.1093/comjnl/17.4.324openalex-snapshot
The Art of Computer Programming, Volume 3, Sorting and Searching
inferredcites →https://doi.org/10.1093/oso/9780198535645.003.0007openalex-snapshot
The multifrontal method in a parallel environment
inferredcites →https://doi.org/10.1137/0611010openalex-snapshot
The Role of Elimination Trees in Sparse Factorization
inferredcites →https://doi.org/10.1137/0710032openalex-snapshot
Nested Dissection of a Regular Finite Element Mesh
inferredcites →https://doi.org/10.1137/0715069openalex-snapshot
An Automatic Nested Dissection Algorithm for Irregular Finite Element Problems
inferredcites →https://doi.org/10.1137/0909021openalex-snapshot
Sparse Cholesky Factorization on a Local-Memory Multiprocessor
inferredcites →https://doi.org/10.1137/1031001openalex-snapshot
The Evolution of the Minimum Degree Ordering Algorithm
inferredcites →https://doi.org/10.1145/214392.214398openalex-snapshot
Modification of the minimum-degree algorithm by multiple elimination
inferredcites →https://doi.org/10.1145/6497.6499openalex-snapshot
A compact row storage scheme for Cholesky factors using elimination trees
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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Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering
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Using domain decomposition to solve symmetric, positive‐definite systems on the hypercube computer
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Run-Time Techniques for Exploiting Irregular Task Parallelism on Distributed Memory Architectures
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PaStiX: A Parallel Sparse Direct Solver Based on a Static Scheduling for Mixed 1D/2D Block Distributions
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A Mapping and Scheduling Algorithm for Parallel Sparse Fan-In Numerical Factorization⋆
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Parallel sparse Cholesky factorization
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Unstructured graph partitioning for sparse linear system solving
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Scalable Parallel Algorithms for Sparse Linear Systems
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Parallel Solution Alternatives for Sparse Triangular Systems in Interior Point Methods
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Scalable Parallel Algorithms for Unstructured Problems
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Parallel Cholesky Factorization for Banded Matrices Using OpenMP Tasks
inferred← citeshttps://doi.org/10.1007/978-3-319-21909-7_7openalex-snapshot
Dynamic Parallelization Strategies for Multifrontal Sparse Cholesky Factorization
inferred← citeshttps://doi.org/10.1007/978-3-540-74466-5_80openalex-snapshot
Task Scheduling for Parallel Multifrontal Methods
inferred← citeshttps://doi.org/10.1007/978-3-642-78123-0_25openalex-snapshot
Eine parallele Implementation des Karmarkar—Verfahrens
inferred← citeshttps://doi.org/10.1007/bfb0031609openalex-snapshot
Sparse matrix ordering with Scotch
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Hybridizing nested dissection and halo approximate minimum degree for efficient sparce matrix ordering
inferred← citeshttps://doi.org/10.1007/bfb0100711openalex-snapshot
Processor allocation and task scheduling to minimize distributed sparse cholesky factorization time
inferred← citeshttps://doi.org/10.1016/0167-8191(92)90014-xopenalex-snapshot
Parallel sparse Cholesky factorization on a shared memory multiprocessor
inferred← citeshttps://doi.org/10.1016/0167-8191(92)90031-2openalex-snapshot
A parallel algorithm for elimination tree computation and symbolic factorization
inferred← citeshttps://doi.org/10.1016/0167-8191(93)90048-popenalex-snapshot
Parallel algorithms for sparse triangular system solution
inferred← citeshttps://doi.org/10.1016/j.parco.2005.07.004openalex-snapshot
Hybrid scheduling for the parallel solution of linear systems
inferred← citeshttps://doi.org/10.1016/j.parco.2014.02.003openalex-snapshot
A study of shared-memory parallelism in a multifrontal solver
inferred← citeshttps://doi.org/10.1016/s0045-7825(99)00242-xopenalex-snapshot
Multifrontal parallel distributed symmetric and unsymmetric solvers
inferred← citeshttps://doi.org/10.1016/s0167-8191(01)00136-3openalex-snapshot
Parallel computation of pseudospectra of large sparse matrices
inferred← citeshttps://doi.org/10.1016/s0167-8191(01)00141-7openalex-snapshot
PaStiX: a high-performance parallel direct solver for sparse symmetric positive definite systems
inferred← citeshttps://doi.org/10.1016/s0167-8191(03)00099-1openalex-snapshot
Impact of reordering on the memory of a multifrontal solver
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
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Gaussian elimination for the solution of linear systems of equations
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A survey of direct methods for sparse linear systems
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Fast Sparse Cholesky Decomposition and Inversion using Nested Dissection Matrix Reordering
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Two-dimensional block partitionings for the parallel sparse Cholesky factorization
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Direct Methods for Sparse Matrices
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Glossary of Symbols
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Copyright Page
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Preface
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Introduction
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Sparse matrices: storage schemes and simple operations
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Gaussian elimination for dense matrices: the algebraic problem
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Gaussian elimination for dense matrices: numerical considerations
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Gaussian elimination for sparse matrices: an introduction
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Reduction to block triangular form
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Local pivotal strategies for sparse matrices
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Ordering sparse matrices for band solution
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Orderings based on dissection
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Implementing Gaussian elimination without 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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Highly scalable parallel algorithms for sparse matrix factorization
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Using Domain Decomposition to Solve Positive-Definite Systems on the Hypercube Computer
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Task-Based Multifrontal QR Solver for GPU-Accelerated Multicore Architectures
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Fast and Accurate Simulation of Multithreaded Sparse Linear Algebra Solvers
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On the memory usage of a parallel multifrontal solver
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Memory-based scheduling for a parallel multifrontal solver
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An automatic clustering algorithm using factorisation tree for parallel power system simulation
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Implementation of parallel algorithms for transient stability analysis on a message passing multicomputer
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A reordering and mapping algorithm for parallel sparse Cholesky factorization
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Techniques for improving the performance of sparse matrix factorization on multiprocessor workstations
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A scalable parallel algorithm for sparse Cholesky factorization
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Reliability-Aware Runtime Adaption Through a Statically Generated Task Schedule
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A Mapping Algorithm for Parallel Sparse Cholesky Factorization
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An Efficient Block-Oriented Approach to Parallel Sparse Cholesky Factorization
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On Computing Inverse Entries of a Sparse Matrix in an Out-of-Core Environment
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Parallel Computation of Entries of ${A}^{-1}$
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Task Scheduling in an Asynchronous Distributed Memory Multifrontal Solver
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A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
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Effects of partitioning and scheduling sparse matrix factorization on communication and load balance
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An efficient block-oriented approach to parallel sparse Cholesky factorization
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Algorithm 915, SuiteSparseQR
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Scaling the solution of large sparse linear systems using multifrontal methods on hybrid shared-distributed memory architectures
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