HSL_MA57
Sparse Symmetric Solver
HSL_MA57 is designed to solve symmetric sparse linear systems efficiently and is particularly powerful for indefinite matrices.
Functionality
- Implements a multifrontal algorithm to solve sparse symmetric systems Ax=b using the factorization A = (PL)D(PL)T.
- Fully integrated package offering: scaling, ordering, error determination, iterative refinement and condition number estimation.
- Special attention has been paid to the factorization of singular or near-singular matrices.
- Options particularly useful to optimization codes, including computation of inertia, and the ability to factorize a nearby positive definite matrix.
- Threshold partial pivoting and static pivoting options.
- Can solve the related systems PLx = b, Dx = b, (PL)Tx = b, and D(PL)Tx = b, with single or multiple right-hand sides.
Performance
- Our most popular serial code for solving sparse symmetric systems.
- A version is currently used by MATLAB for factorizing sparse indefinite systems.
- The optimization code IPOPT provides an interface for HSL_MA57.
- Competitive factorization time for indefinite systems and a fast solve time for repeated solution of equations with the same matrix but differing right-hand sides.
- Significantly faster than its still widely used predecessor MA27.
Numerical results are presented in [1].
Availability
We offer both in-house usage and incorporation licences for HSL_MA57. It is freely available for academic use. Please see our website, or email us at hsl@stfc.ac.uk for further details.
[1] I. S. Duff (2004), MA57 --- A code for the solution of sparse symmetric indefinite systems, ACM Transactions on Math Softw 30 (2), 118-144.