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A Fan-In Algorithm for Distributed Sparse Numerical Factorization

https://doi.org/10.1137/0911033
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Outgoing claims: the papers this work cites, builds on, or argues with.

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(88)90009-9openalex-snapshot
Parallel solution of triangular systems of equations
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/10.1137/0710032openalex-snapshot
Nested Dissection of a Regular Finite Element Mesh
inferredcites →https://doi.org/10.1137/0909021openalex-snapshot
Sparse Cholesky Factorization on a Local-Memory Multiprocessor
inferredcites →https://doi.org/10.1137/0912063openalex-snapshot
Limiting Communication in Parallel Sparse Cholesky Factorization
inferredcites →https://doi.org/10.1177/109434208700100304openalex-snapshot
Concurrent Multifrontal Methods: Shared Memory, Cache, and Frontwidth Issues
inferredcites →https://doi.org/10.1177/109434208700100403openalex-snapshot
Progress in Sparse Matrix Methods for Large Linear Systems On Vector Supercomputers

What points at this work

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

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Multiprocessors and run‐time compilation
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An organization of sparse gauss elimination for solving partial differntial equations on distributed memory machines
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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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The Fan-Both Family of Column-Based Distributed Cholesky Factorization Algorithms
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Scalability of Sparse Direct Solvers
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Parallel Direct Solution of Sparse Linear Systems
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Eine parallele Implementation des Karmarkar—Verfahrens
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Parallel Direct Methods for Sparse Linear Systems
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An incomplete nested dissection algorithm for parallel direct solution of finite element discretizations of partial differential equations
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Parallel implementation of finite-element/newton method for solution of steady-state and transient nonlinear partial differential equations
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A parallel sparse LU decomposition with application to semiconductor device simulation
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Parallel sparse Cholesky factorization on a shared memory multiprocessor
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Software support for irregular and loosely synchronous problems
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PARTI primitives for unstructured and block structured problems
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Distributed Memory Compiler Methods for Irregular Problems – Data Copy Reuse and Runtime Partitioning1 1This work is supported by NASA contract NAS1-18605 while the authors were in residence at ICASE, NASA Langley Research Center. In addition, support for author Saltz was provided by NSF from NSF…
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PaStiX: a high-performance parallel direct solver for sparse symmetric positive definite systems
inferred← citeshttps://doi.org/10.1016/s0167-8191(99)00077-0openalex-snapshot
Developments and trends in the parallel solution of linear systems
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References
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Gaussian elimination for the solution of linear systems of equations
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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 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 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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Distributed asynchronous Cholesky decomposition
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Parti Procedures for Realistic Loops
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Supernodal Sparse Cholesky Factorization on Distributed-Memory Multiprocessors
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Scheduling Strategies for Sparse Cholesky Factorization on a Shared Virtual Memory Parallel Computer
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Techniques for improving the performance of sparse matrix factorization on multiprocessor workstations
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Performance of distributed sparse Cholesky factorization with pre-scheduling
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A scalable parallel algorithm for sparse Cholesky factorization
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Parallel Hybrid Preconditioning: Incomplete Factorization with Selective Sparse Approximate Inversion
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Limiting Communication in Parallel Sparse Cholesky Factorization
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A Grid-Based Subtree-Subcube Assignment Strategy for Solving Partial Differential Equations on Hypercubes
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A Mapping Algorithm for Parallel Sparse Cholesky Factorization
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Parallel Algorithms for Sparse Linear Systems
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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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