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
ACM Transactions on Mathematical Software (TOMS)
Sparse matrices in matlab: design and implementation
SIAM Journal on Matrix Analysis and Applications
Exploiting structural symmetry in a sparse partial pivoting code
SIAM Journal on Scientific Computing
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
The implementation of the Cilk-5 multithreaded language
PLDI '98 Proceedings of the ACM SIGPLAN 1998 conference on Programming language design and implementation
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
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
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Graph separator theorems and sparse gaussian elimination
Graph separator theorems and sparse gaussian elimination
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Parallel and fully recursive multifrontal sparse Cholesky
Future Generation Computer Systems - Special issue: Selected numerical algorithms
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)
A supernodal out-of-core sparse Gaussian-elimination method
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Design of a Multicore Sparse Cholesky Factorization Using DAGs
SIAM Journal on Scientific Computing
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We present a new parallel sparse LU factorization algorithm and code. The algorithm uses a column-preordering partial-pivoting unsymmetric-pattern multifrontal approach. Our baseline sequential algorithm is based on UMFPACK 4, but is somewhat simpler and is often somewhat faster than UMFPACK version 4.0. Our parallel algorithm is designed for shared-memory machines with a small or moderate number of processors (we tested it on up to 32 processors). We experimentally compare our algorithm with SuperLU_MT, an existing shared-memory sparse LU factorization with partial pivoting. SuperLU_MT scales better than our new algorithm, but our algorithm is more reliable and is usually faster. More specifically, on matrices that are costly to factor, our algorithm is usually faster on up to 4 processors, and is usually faster on 8 and 16. We were not able to run SuperLU_MT on 32. The main contribution of this article is showing that the column-preordering partial-pivoting unsymmetric-pattern multifrontal approach, developed as a sequential algorithm by Davis in several recent versions of UMFPACK, can be effectively parallelized.