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Version 3.11.3

1st November 2023

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 an \(n \times s\) matrix \(\mathbf{B}\)), this subroutine solves the system \(\mathbf{Ax}=\mathbf{b}\) (\(\mathbf{AX}=\mathbf{B}\)). The matrix \(\mathbf{A}\) need not be definite.

The multifrontal method is used. It 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.