A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM Journal on Matrix Analysis and Applications
Error bounds from extra-precise iterative refinement
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems
International Journal of High Performance Computing Applications
A Note on GMRES Preconditioned by a Perturbed $L D L^T$ Decomposition with Static Pivoting
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
High-performance implementation of the level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Extra-Precise Iterative Refinement for Overdetermined Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
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)
Automatically adapting programs for mixed-precision floating-point computation
Proceedings of the 27th international ACM conference on International conference on supercomputing
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
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On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for using single precision for the solution of linear systems is a potential loss of accuracy in the computed solutions. For sparse linear systems, the use of mixed precision in which double-precision iterative methods are preconditioned by a single-precision factorization can enable the recovery of high-precision solutions more quickly and use less memory than a sparse direct solver run using double-precision arithmetic. In this article, we consider the use of single precision within direct solvers for sparse symmetric linear systems, exploiting both the reduction in memory requirements and the performance gains. We develop a practical algorithm to apply a mixed-precision approach and suggest parameters and techniques to minimize the number of solves required by the iterative recovery process. These experiments provide the basis for our new code HSL_MA79—a fast, robust, mixed-precision sparse symmetric solver that is included in the mathematical software library HSL. Numerical results for a wide range of problems from practical applications are presented.