Predicting fill for sparse orthogonal factorization
Journal of the ACM (JACM)
On general row merging schemes for sparse given transformations
SIAM Journal on Scientific and Statistical Computing
Symbolic factorization for sparse Gaussian elimination with partial pivoting
SIAM Journal on Scientific and Statistical Computing
The WY representation for products of householder matrices
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
A data structure for sparse QR and LU factorizations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
A storage-efficient WY representation for products of householder transformations
SIAM Journal on Scientific and Statistical Computing
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
The multifrontal method and paging in sparse Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Task scheduling for parallel sparse Cholesky factorization
International Journal of Parallel Programming
Incremental condition estimation for sparse matrices
SIAM Journal on Matrix Analysis and Applications
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
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)
Parallel sparse QR factorization on shared memory architectures
Parallel Computing
Parallel Sparse Orthogonal Factorization on Distributed-Memory Multiprocessors
SIAM Journal on Scientific Computing
Multifrontal Computation with the Orthogonal Factors of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
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
Sparse Multifrontal Rank Revealing QR Factorization
SIAM Journal on Matrix Analysis and Applications
ScaLAPACK user's guide
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Modifying a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Unitary Triangularization of a Nonsymmetric Matrix
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
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
Exact Prediction of QR Fill-In by Row-Merge Trees
SIAM Journal on Scientific Computing
Multiple-Rank Modifications of a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
An Unsymmetrized Multifrontal LU Factorization
SIAM Journal on Matrix Analysis and Applications
A software package for sparse orthogonal factorization and updating
ACM Transactions on Mathematical Software (TOMS)
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
A column pre-ordering strategy for the 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)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
High-performance implementation of the level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Intel threading building blocks
Intel threading building blocks
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
Design of a Multicore Sparse Cholesky Factorization Using DAGs
SIAM Journal on Scientific Computing
Fine granularity sparse QR factorization for multicore based systems
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Proceedings of the ACM international conference on Object oriented programming systems languages and applications
Generalized subgraph preconditioners for large-scale bundle adjustment
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
O-snap: Optimization-based snapping for modeling architecture
ACM Transactions on Graphics (TOG)
Potential of General Purpose Graphic Processing Unit for Energy Management System
International Journal of Distributed Systems and Technologies
Feature-Preserved 3D Canonical Form
International Journal of Computer Vision
Algorithm 930: FACTORIZE: An object-oriented linear system solver for MATLAB
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Multifrontal QR factorization for multicore architectures over runtime systems
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
Personal and Ubiquitous Computing
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SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel's Threading Building Blocks library. The symbolic analysis and ordering phase pre-eliminates singletons by permuting the input matrix A into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill-reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of ATA. Approximate rank-detection is performed within each frontal matrix using Heath's method. While Heath's method is not always exact, it has the advantage of not requiring column pivoting and thus does not interfere with the fill-reducing ordering. For sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.