Hybrid sparse-matrix methods

Abstract

In computer-aided design for large systems, the efficient solution of large sparse systems of linear equations is important. We critically examine two parts of the solution of sparse systems of linear equations: ordering and the factorization of the ordered matrix. After examining several candidates from a theoretical point of view, as well as with examples, we conclude that the Markowitz ordering criteria, with extension for the variability-type problem, is the most practical ordering algorithm. A combination of solution processes provides a very efficient hybrid algorithm for factoring the ordered sparse matrix. The hybrid is outlined so that it may be tailored to minimum storage utilization, minimum central processing unit (CPU) time, or may be built entirely in a high-level language to reduce programming time. A number of examples are included.