A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Solving symmetric indefinite systems in an interior-point method for linear programming
Mathematical Programming: Series A and B
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
On the Stability of Cholesky Factorization For Symmetric Quasidefinite Systems
SIAM Journal on Matrix Analysis and Applications
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Accurate Symmetric Indefinite Linear Equation Solvers
SIAM Journal on Matrix Analysis and Applications
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
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
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
A Note on the LDLT Decomposition of Matrices from Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM Journal on Matrix Analysis and Applications
Mathematical Programming: Series A and B
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
SIAM Journal on Scientific Computing
Computational Optimization and Applications
SIAM Journal on Matrix Analysis and Applications
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Partial factorization of a dense symmetric indefinite matrix
ACM Transactions on Mathematical Software (TOMS)
Design of a Multicore Sparse Cholesky Factorization Using DAGs
SIAM Journal on Scientific Computing
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The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen before the factorization begins. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to ensure numerical stability. These modifications can have serious consequences in terms of time as well as the memory and flops required for the factorization and subsequent solves. This study focuses on hard-to-solve sparse symmetric indefinite problems for which standard threshold partial pivoting leads to significant modifications. We perform a detailed review of pivoting strategies that are aimed at reducing the modifications without compromising numerical stability. Extensive numerical experiments are performed on a set of tough problems arising from practical applications. Based on our findings, we make recommendations on which strategy to use and, in particular, a matching-based approach is recommended for numerically challenging problems.