A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
Parallel implementation of multifrontal schemes
Parallel Computing
On the storage requirement in the out-of-core multifrontal method for sparse factorization
ACM Transactions on Mathematical Software (TOMS)
The impact of hardware gather/scatter on sparse Gaussian elimination
SIAM Journal on Scientific and Statistical Computing
ACM Transactions on Mathematical Software (TOMS)
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Squeezing the most out of an algorithm in CRAY FORTRAN
ACM Transactions on Mathematical Software (TOMS)
A New Implementation of Sparse Gaussian Elimination
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
ACM SIGNUM Newsletter
Proposed sparse extensions to the Basic Linear Algebra Subprograms
ACM SIGNUM Newsletter
A generalized envelope method for sparse factorization by rows
ACM Transactions on Mathematical Software (TOMS)
Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
Task scheduling using a block dependency DAG for block-oriented sparse Cholesky factorization
SAC '00 Proceedings of the 2000 ACM symposium on Applied computing - Volume 2
Improved load distribution in parallel sparse cholesky factorization
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Estimating Computer Performance for Parallel Sparse QR Factorisation
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
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
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
Hypermatrix oriented supernode amalgamation
The Journal of Supercomputing
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
Multifrontal computations on GPUs and their multi-core hosts
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Optimization of a statically partitioned hypermatrix sparse cholesky factorization
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Gigaflops in linear programming
Operations Research Letters
Managing data-movement for effective shared-memory parallelization of out-of-core sparse solvers
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Computers & Mathematics with Applications
Hi-index | 0.00 |
In this paper we present an algorithm for partitioning the nodes of a graph into supernodes, which improves the performance of the multifrontal method for the factorization of large, sparse matrices on vector computers. This new algorithm first partitions the graph into fundamental supernodes. Next, using a specified relaxation parameter, the supernodes are coalesced in a careful manner to create a coarser supernode partition. Using this coarser partition in the factorization generally introduces logically zero entries into the factor. This is accompanied by a decrease in the amount of sparse vector computations and data movement and an increase in the number of dense vector operations. The amount of storage required for the factor is generally increased by a small amount. On a collection of moderately sized 3-D structures, matrices speedups of 3 to 20 percent on the Cray X-MP are observed over the fundamental supernode partition which allows no logically zero entries in the factor. Using this relaxed supernode partition, the multifrontal method now factorizes the extremely sparse electric power matrices faster than the general sparse algorithm. In addition, there is potential for considerably reducing the communication requirements for an implementation of the multifrontal method on a local memory multiprocessor.