A new polynomial-time algorithm for linear programming
Combinatorica
Predicting fill for sparse orthogonal factorization
Journal of the ACM (JACM)
Distribution of mathematical software via electronic mail
Communications of the ACM
Symbolic factorization for sparse Gaussian elimination with partial pivoting
SIAM Journal on Scientific and Statistical Computing
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A generalized envelope method for sparse factorization by rows
ACM Transactions on Mathematical Software (TOMS)
Sparse matrices in matlab: design and implementation
SIAM Journal on Matrix Analysis and Applications
Sparse matrix methods for chemical process separation calculations on supercomputers
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Sparsity analysis of the QR factorization
SIAM Journal on Matrix Analysis and Applications
An Efficient Algorithm to Compute Row and Column Counts for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Compressed graphs and the minimum degree algorithm
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Node Selection Strategies for Bottom-Up Sparse Matrix Ordering
SIAM Journal on Matrix Analysis and Applications
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Performance of Greedy Ordering Heuristics for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
ACM Transactions on Mathematical Software (TOMS)
On Algorithms for Obtaining a Maximum Transversal
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Algebraic analysis of high-pass quantization
ACM Transactions on Graphics (TOG)
Using dense storage to solve small sparse linear systems
ACM Transactions on Mathematical Software (TOMS)
Parallel sparse LU factorization on different message passing platforms
Journal of Parallel and Distributed Computing
ACM Transactions on Mathematical Software (TOMS)
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing
International Journal of Robotics Research
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Neural Networks for Predicting the Behavior of Preconditioned Iterative Solvers
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
On Using Reinforcement Learning to Solve Sparse Linear Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Online Sparse Matrix Gaussian Process Regression and Vision Applications
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Probabilistic structure matching for visual SLAM with a multi-camera rig
Computer Vision and Image Understanding
3D mapping for urban service robots
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems
ACM Transactions on Mathematical Software (TOMS)
A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting
ACM Transactions on Mathematical Software (TOMS)
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices
SIAM Journal on Scientific Computing
iSAM2: Incremental smoothing and mapping using the Bayes tree
International Journal of Robotics Research
Using performance profiles to evaluate preconditioners for iterative methods
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
Progress toward multi-robot reconnaissance and the MAGIC 2010 competition
Journal of Field Robotics
A fast time-domain EM-TCAD coupled simulation framework via matrix exponential
Proceedings of the International Conference on Computer-Aided Design
Algorithm 930: FACTORIZE: An object-oriented linear system solver for MATLAB
ACM Transactions on Mathematical Software (TOMS)
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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Sparse Gaussian elimination with partial pivoting computes the factorization PAQ = LU of a sparse matrix A, where the row ordering P is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, Q, based solely on the nonzero pattern of A, that limits the worst-case number of nonzeros in the factorization. The fill-in also depends on P, but Q is selected to reduce an upper bound on the fill-in for any subsequent choice of P. The choice of Q can have a dramatic impact on the number of nonzeros in L and U. One scheme for determining a good column ordering for A is to compute a symmetric ordering that reduces fill-in in the Cholesky factorization of ATA. A conventional minimum degree ordering algorithm would require the sparsity structure of ATA to be computed, which can be expensive both in terms of space and time since ATA may be much denser than A. An alternative is to compute Q directly from the sparsity structure of A; this strategy is used by MATLAB's COLMMD preordering algorithm. A new ordering algorithm, COLAMD, is presented. It is based on the same strategy but uses a better ordering heuristic. COLAMD is faster and computes better orderings, with fewer nonzeros in the factors of the matrix.