## Version 1.0.0

12th July 2004

Recent Changes

Given the sparsity pattern of an $$n \times n$$ symmetric matrix $$\mathbf{A}$$ and a symmetric permutation that reduces the profile of $$\mathbf{A}$$, this routine computes a new symmetric permutation with a smaller profile. The exchange algorithms of Hager are used to refine the given permutation.
Any zeros on the diagonal of $$\mathbf{A}$$ are regarded as nonzero. If $$m_i$$ is the column index of the first nonzero in row $$i$$ ($$m _i \le i$$), the length of row $$i$$ is $$i - m _i + 1$$ and the profile of $$\mathbf{A}$$ is the sum of the lengths of the rows.
MC61 (or MC60) may be used to obtain an initial symmetric permutation.