On the number of nonzeros added when Gaussian elimination is performed on sparse random matrices

Abstract

This paper studies the fill-in properties of Gaussian elimination on sparse random matrices. A theoretical study using the concept of random graphs yields formulae from which the fill-in can be evaluated. The predictions are examined for matrices of various orders and densities and are found to be in close agreement with experimental results. A possible consequence of the results of this paper relating to error analysis for sparse systems is given in the concluding section.