MA67: Sparse symmetric system, zeros on diagonal: blocked conventional

To solve a sparse symmetric indefinite system of linear equations. Given a sparse symmetric matrix \(\mathbf{A} = {\{a _{ij}\}} _{n \times n}\) and an \(n\)-vector \(\mathbf{b}\), this subroutine solves the system \(\mathbf{Ax} = \mathbf{b}\).

The method used is a direct method using an \(\mathbf {LD L} ^T\) factorization, where \(\mathbf{L}\) is unit lower triangular and \(\mathbf{D}\) is block diagonal with blocks of order 1 and 2. Advantage is taken of the extra sparsity available with \(2 \times 2\) pivots (blocks of \(\mathbf{D}\)) with one or both diagonal entries of value zero. The numerical values of the entries are taken in account during the first choice of pivots.