HSL_MA57: Sparse symmetric system: multifrontal method

To solve a sparse symmetric system of linear equations. Given a sparse symmetric matrix $\mathbf{A}={\{a_{ij}\}}_{n\times n}$ and an $n$-vector $\mathbf{b}$ or a matrix $\mathbf{B}={\{b_{ij}\}}_{n\times r}$, this subroutine solves the system $\mathbf{Ax}=\mathbf{b}$ or the system $\mathbf{AX}=\mathbf{B}$ . The matrix $\mathbf{A}$ need not be definite. There is an option for iterative refinement.

The method used is a direct method based on a sparse variant of Gaussian elimination.

The matrix is optionally prescaled by using a symmetrization of the MC64 scaling. Other ordering options are provided including hooks to MeTiS. The user can avoid additional fill-in to that predicted by the analysis by using static pivoting.

There are facilities for returning a Fredholm vector, multiplying a vector by the factors, exploiting sparse right-hand sides, and returning factors in standard format.