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Symbolic Factorization for Sparse Gaussian Elimination with Partial Pivoting
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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An Optimal Agorithm for Symbolic Factorization of Symmetric Matrices
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Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems
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A Comparison of Some Methods for Solving Sparse Linear Least-Squares Problems
inferredcites →https://doi.org/10.1137/0906028openalex-snapshot
An Implementation of Gaussian Elimination with Partial Pivoting for Sparse Systems
inferredcites →https://doi.org/10.1145/214392.214398openalex-snapshot
Modification of the minimum-degree algorithm by multiple elimination
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Some Design Features of a Sparse Matrix Code
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On Algorithms for Obtaining a Maximum Transversal
inferredcites →https://doi.org/10.1145/5925.5932openalex-snapshot
Predicting fill for sparse orthogonal factorization
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Combinatorial Aspects in Sparse Elimination Methods
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Prestructuring sparse matrices with dense rows and columns via null space methods
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Predicting Structure in Nonsymmetric Sparse Matrix Factorizations
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The Use of Vector and Parallel Computers in the Solution of Large Sparse Linear Equations
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Direct Methods for Linear Systems
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Linear Least Squares Problems
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Using Random Butterfly Transformations to Avoid Pivoting in Sparse Direct Methods
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Solution of Sparse Systems of Equations on Multiprocessor Architectures
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Algorithms for Solving Nonlinear Systems of Equations
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Evaluating the performance of algebraic operations on storage schemes for large sparse matrices
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Parallel sparse Gaussian elimination with partial pivoting
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PARASPAR: Parallel solvers for sparse linear algebraic systems
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Solution of sparse systems of equations on multiprocessor architectures
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On the row merge tree for sparse LU factorization with partial pivoting
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Predicting the structure of sparse orthogonal factors
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An extension of the theory of secant preconditioners
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Parallel sparse LU factorization on different message passing platforms
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Mixed and componentwise condition numbers for matrix decompositions
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Practical quasi-Newton methods for solving nonlinear systems
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/10.1023/a:1021943902025openalex-snapshot
Computing Row and Column Counts for Sparse QR and LU Factorization
inferred← citeshttps://doi.org/10.1051/m2an/1992260203091openalex-snapshot
The column-updating method for solving nonlinear equations in Hilbert space
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Solving nonlinear systems of equations by means of quasi-neston methods with a nonmonotone stratgy∗
inferred← citeshttps://doi.org/10.1090/s0025-5718-1993-1176714-xopenalex-snapshot
A theory of secant preconditioners
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
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Copyright Page
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
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Pictures of sparse matrices
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198508380.005.0003openalex-snapshot
Solutions to selected exercises
inferred← citeshttps://doi.org/10.1109/71.663864openalex-snapshot
Efficient sparse LU factorization with partial pivoting on distributed memory architectures
inferred← citeshttps://doi.org/10.1109/iecon55916.2024.10905751openalex-snapshot
Sparse Linear Solvers for Large-scale Electromagnetic Transient Simulations
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Using postordering and static symbolic factorization for parallel sparse LU
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A Low Complexity-High Throughput QC-LDPC Encoder
inferred← citeshttps://doi.org/10.1137/050629343openalex-snapshot
Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting
inferred← citeshttps://doi.org/10.1137/0611010openalex-snapshot
The Role of Elimination Trees in Sparse Factorization
inferred← citeshttps://doi.org/10.1137/0614046openalex-snapshot
Sparsity Analysis of the $QR$ Factorization
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Error Bounds for the Computation of Null Vectors with Applications to Markov Chains
inferred← citeshttps://doi.org/10.1137/0909008openalex-snapshot
A Data Structure for Sparse $QR$ and $LU$ Factorizations
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On the Complexity of Sparse $QR$ and $LU$ Factorization of Finite-Element Matrices
inferred← citeshttps://doi.org/10.1137/0912062openalex-snapshot
A Scheme for Handling Rank-Deficiency in the Solution of Sparse Linear Least Squares Problems
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Comparing Algorithms for Solving Sparse Nonlinear Systems of Equations
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Distributed Sparse Gaussian Elimination and Orthogonal Factorization
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The Evolution of the Minimum Degree Ordering Algorithm
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Solving Mixed Sparse-Dense Linear Least-Squares Problems by Preconditioned Iterative Methods
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A Note on the Column Elimination Tree
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Predicting Structure in Sparse Matrix Computations
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Some Results on Structure Prediction in Sparse $QR$ Factorization
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A Supernodal Approach to Sparse Partial Pivoting
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An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
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S + : Efficient 2D Sparse LU Factorization on Parallel Machines
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Exact Prediction of QR Fill-In by Row-Merge Trees
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A column approximate minimum degree ordering algorithm
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Parallel sparse LU factorization on second-class message passing platforms
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Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
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Sparse LU factorization with partial pivoting on distributed memory machines
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A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
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A tight and explicit representation of Q in sparse QR factorization
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A tight and explicit representation of Q in sparse QR factorization
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Predicting structure in nonsymmetric sparse matrix factorizations
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Diferenciação computacional e aplicações
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Estudio de librerías paralelas de libre distribución y algoritmos paralelos iterativos multipaso para la resolución de sistemas de ecuaciones lineales dispersos. Aplicación a la ecuación de difusión neutrónica.
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Combler l’écart entre H-Matrices et méthodes directes creuses pour la résolution de systèmes linéaires de grandes tailles
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