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.