## Version 5.2.0

2nd August 2013

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### HSL_MA57 Sparse symmetric system: multifrontal method

To solve a sparse symmetric system of linear equations. Given a sparse symmetric matrix $A={\left\{{a}_{ij}\right\}}_{n×n}$ and an $n$-vector $b$ or a matrix $B={\left\{{b}_{ij}\right\}}_{n×r}$, this subroutine solves the system $Ax=b$ or the system $AX=B$ . The matrix $A$ 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.