Solution of a sparse linear system by using digraph

Abstract

In this work, a method is given to compute solution of a sparse system of linear equations using Cramer's rule. The solution is computed with the help of digraph approach given in Chen, wherein only the non-zero entries are used. Only integer entries including right hand side are considered. We show that efficiency with which a sparse linear system can be analyzed by digital computer using digraph approach as a tool depends largely upon the efficiency with which 1-factors and 1-factorial connections are generated. Finally, the usefulness of digraph approach is discussed. The program is experimented by applying on three examples.