A Fast Implementation of the Minimum Degree Algorithm Using Quotient Graphs
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
A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
A graph partitioning algorithm by node separators
ACM Transactions on Mathematical Software (TOMS)
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 generalized envelope method for sparse factorization by rows
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Effects of partitioning and scheduling sparse matrix factorization on communication and load balance
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Towards a fast implementation of spectral nested dissection
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Performance of distributed sparse Cholesky factorization with pre-scheduling
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Analysis of multilevel graph partitioning
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
A Parallel Interior Point Method and Its Application to Facility Location Problems
Computational Optimization and Applications
Tradeoffs between parallelism and fill in nested dissection
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
The generic graph component library
Proceedings of the 14th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
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
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
The design of I/O-efficient sparse direct solvers
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Improved load distribution in parallel sparse cholesky factorization
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Finding Optimal Ordering of Sparse Matrices for Column-Oriented Parallel Cholesky Factorization
The Journal of Supercomputing
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
The Interior-Point Method for Linear Programming
IEEE Software
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Parallel Multilevel Graph Partitioning
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
An Object-Oriented Collection of Minimum Degree Algorithms
ISCOPE '98 Proceedings of the Second International Symposium on Computing in Object-Oriented Parallel Environments
A new scheduling algorithm for parallel sparse LU factorization with static pivoting
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
FaSa: a fast and stable quadratic placement algorithm
Journal of Computer Science and Technology
Impact of reordering on the memory of a multifrontal solver
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
A column 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
Improving Parallel Ordering of Sparse Matrices Using Genetic Algorithms
Applied Intelligence
RCLK-VJ network reduction with Hurwitz polynomial approximation
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Static load balancing applied to Schur complement method
Computers and Structures
ACM Transactions on Mathematical Software (TOMS)
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
Applied Numerical Mathematics
Management of services based on a semantic description within the GRID-TLSE project
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Fill-ins number reducing direct solver designed for FIT-type matrix
Mathematics and Computers in Simulation
A robust ILU preconditioner using constraints diagonal Markowitz
Proceedings of the 48th Annual Southeast Regional Conference
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization
SIAM Journal on Scientific Computing
Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices
SIAM Journal on Scientific Computing
Selector: a language construct for developing dynamic applications
LCPC'02 Proceedings of the 15th international conference on Languages and Compilers for Parallel Computing
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Fully dynamic algorithm for chordal graphs with O(1) query-time and O(n 2) update-time
Theoretical Computer Science
Recovering an optimal LP basis from an interior point solution
Operations Research Letters
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.01 |
The most widely used ordering scheme to reduce fills and operations in sparse matrix computation is the minimum-degree algorithm. The notion of multiple elimination is introduced here as a modification to the conventional scheme. The motivation is discussed using the k-by-k grid model problem. Experimental results indicate that the modified version retains the fill-reducing property of (and is often better than) the original ordering algorithm and yet requires less computer time. The reduction in ordering time is problem dependent, and for some problems the modified algorithm can run a few times faster than existing implementations of the minimum-degree algorithm. The use of external degree in the algorithm is also introduced.