A spectral algorithm for envelope reduction of sparse matrices

Abstract

A new algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK's reverse Cuthill-McKee (RCM).