Predicting fill for sparse orthogonal factorization
Journal of the ACM (JACM)
Direct methods for sparse matrices
Direct methods for sparse matrices
Symbolic factorization for sparse Gaussian elimination with partial pivoting
SIAM Journal on Scientific and Statistical Computing
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Exploiting structural symmetry in unsymmetric sparse symbolic factorization
SIAM Journal on Matrix Analysis and Applications
Sparse matrices in matlab: design and implementation
SIAM Journal on Matrix Analysis and Applications
Sparse QR factorization in MATLAB
ACM Transactions on Mathematical Software (TOMS)
A Cartesian Parallel Nested Dissection Algorithm
SIAM Journal on Matrix Analysis and Applications
The design of a new frontal code for solving sparse, unsymmetric systems
ACM Transactions on Mathematical Software (TOMS)
The design of MA48: a code for the direct solution of sparse unsymmetric linear systems of equations
ACM Transactions on Mathematical Software (TOMS)
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
Robust Ordering of Sparse Matrices using Multisection
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Improving the Run Time and Quality of Nested Dissection Ordering
SIAM Journal on Scientific Computing
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
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)
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Nested-Dissection Orderings for Sparse LU with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
An Unsymmetrized Multifrontal LU Factorization
SIAM Journal on Matrix Analysis and Applications
Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
On the lu factorization of sequences of identically structured sparse matrices within a distributed memory environment
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A column approximate minimum degree ordering algorithm
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)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
On the Spatial Statistics of Optical Flow
International Journal of Computer Vision
Exploring weak scalability for FEM calculations on a GPU-enhanced cluster
Parallel Computing
PyTrilinos: High-performance distributed-memory solvers for Python
ACM Transactions on Mathematical Software (TOMS)
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
On the design of interfaces to sparse direct solvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
A multi-level parallel simulation approach to electron transport in nano-scale transistors
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
A Sketch-Based Interface for Modeling Myocardial Fiber Orientation
SG '07 Proceedings of the 8th international symposium on Smart Graphics
Using GPUs to improve multigrid solver performance on a cluster
International Journal of Computational Science and Engineering
Applied Numerical Mathematics
Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU
International Journal of Computational Science and Engineering
Algorithms for the balanced edge partitioning problem
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
A supernodal out-of-core sparse Gaussian-elimination method
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A Parallel Implementation of Electron-Phonon Scattering in Nanoelectronic Devices up to 95k Cores
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
Atomistic nanoelectronic device engineering with sustained performances up to 1.44 PFlop/s
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Content aware video manipulation
Computer Vision and Image Understanding
A CPU-GPU hybrid approach for the unsymmetric multifrontal method
Parallel Computing
Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
SIAM Journal on Scientific Computing
A Contour Integral Method for the Black-Scholes and Heston Equations
SIAM Journal on Scientific Computing
Developing a dynamic model of cascading failure for high performance computing using trilinos
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
Model order reduction for large scale engineering models developed in ANSYS
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Algorithm 930: FACTORIZE: An object-oriented linear system solver for MATLAB
ACM Transactions on Mathematical Software (TOMS)
Advances in Engineering Software
An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods
Journal of Computational and Applied Mathematics
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
Computers & Mathematics with Applications
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A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-in and then refined during numerical factorization (while preserving the bound). Pivot rows are selected to maintain numerical stability and to preserve sparsity. The method analyzes the matrix and automatically selects one of three pre-ordering and pivoting strategies. The number of nonzeros in the LU factors computed by the method is typically less than or equal to those found by a wide range of unsymmetric sparse LU factorization methods, including left-looking methods and prior multifrontal methods.