HSL_MA48
Sparse Unsymmetric Solver
HSL_MA48 is designed to solve unsymmetric sparse linear systems efficiently. It is particularly powerful for solving systems that are structurally unsymmetric and highly sparse.
Note: For unsymmetric but structurally symmetric systems, MA41 may be used. An MPI version is available as HSL_MP48.
Functionality
- Implements Markowitz with threshold pivoting to solve sparse unsymmetric systems Ax=b using Gaussian elimination A = PL(UQ). For reducible systems, the block triangular form can be detected and exploited.
- Option to solve transpose systems ATx=b
- A can be square or rectangular.
- Built-in iterative refinement, computation of backward and forward errors and the matrix condition number estimation.
- Ability to reuse previously determined pivot sequence in subsequent solves, or factorize only a part of the matrix.
Performance
- Our market-leading code for sparse unsymmetric unstructured systems, used in many major industrial codes.
- Competitive factorization time.
- Fast solution phase.
Numerical results are presented in [1] and [2].
Availability
We offer both in-house usage and incorporation licences for HSL_MA48. 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 and J. K. Reid (1993), MA48, a Fortran code for direct solution of sparse unsymmetric linear systems of equations, Technical Report RAL-93-072.
[2] I. S. Duff and J. K. Reid (1995), The design of MA48, a code for the direct solution of sparse unsymmetric linear systems of equations, ACM Trans on Math Softw 22 (2), 187-226.