An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The design of a new frontal code for solving sparse, unsymmetric systems
ACM Transactions on Mathematical Software (TOMS)
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
The growth factor and efficiency of Gaussian elimination with rook pivoting
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Scaling for Numerical Stability in Gaussian Elimination
Journal of the ACM (JACM)
Efficient Methods for Out-of-Core Sparse Cholesky Factorization
SIAM Journal on Scientific Computing
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
The design and implementation of a new out-of-core sparse cholesky factorization method
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)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM Journal on Matrix Analysis and Applications
A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting
SIAM Journal on Scientific Computing
Algorithm 891: A Fortran virtual memory system
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
Partial factorization of a dense symmetric indefinite matrix
ACM Transactions on Mathematical Software (TOMS)
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Out-of-core sparse direct solvers reduce the amount of main memory needed to factorize and solve large sparse linear systems of equations by holding the matrix data, the computed factors, and some of the work arrays in files on disk. The efficiency of the factorization and solution phases is dependent upon the number of entries in the factors. For a given pivot sequence, the level of fill in the factors beyond that predicted on the basis of the sparsity pattern alone depends on the number of pivots that are delayed (i.e., the number of pivots that are used later than expected because of numerical stability considerations). Our aim is to limit the number of delayed pivots, while maintaining robustness and accuracy. In this article, we consider a new out-of-core multifrontal solver HSL_MA78 from the HSL mathematical software library that is designed to solve the unsymmetric sparse linear systems that arise from finite element applications. We consider how equilibration can be built into the solver without requiring the system matrix to be held in main memory. We also examine the effects of different pivoting strategies, including threshold partial pivoting, threshold rook pivoting, and static pivoting. Numerical experiments on problems arising from a range of practical applications illustrate the importance of scaling and show that, in some cases, rook pivoting can be more efficient than partial pivoting in terms of both the factorization time and the sparsity of the computed factors.