MA41: Sparse unsymmetric system: unsymmetric multifrontal method

To solve a sparse unsymmetric system of linear equations. Given an unsymmetric square sparse matrix \(\mathbf{A}\) of order \(n\) and an \(n\)-vector \(\mathbf{B}\), this subroutine solves the system \(\mathbf{Ax}=\mathbf{b}\) or \(\mathbf{A} ^T \mathbf{x} = \mathbf{b}\). The method used is a parallel direct method based on a sparse multifrontal variant of Gaussian elimination. An initial ordering for the pivotal sequence is chosen using the pattern of the matrix \(\mathbf A\) + \(\mathbf A ^T\) and is later modified for reasons of numerical stability. Thus this code performs best on matrices whose pattern is symmetric, or nearly so. For symmetric sparse matrices or for very unsymmetric and very sparse matrices, other software might be more appropriate (for example, MA57 or MA48).