(An) ordering algorithm to obtain a minimal fill-in of sparse matrix

Abstract

In this paper, a graph theoretic elimination process which models Gaussian elimination on sparse system of linear equations is considered. The theoretical results and efficient algorithms based on graph theory are presented. Then these algorithms are combined into a more general ordering algorithm which produces a perfect ordering if one exists, or a minimal fill-in, otherwise. This algorithm is implemented on NOVA-840 and compared with other ordering algorithms, the minimum degree ordering algorithm and the minimum deficiency ordering algorithm. the several sample models are tested and their results are included to show how this algorithm works.