Finite sparse matrix techniques. [Solution of linear systems Ax = b]

A unified theory of finite sparse matrix techniques based on a literature search and new results is presented. It is intended to aid in computational work and symbolic manipulation of large sparse systems of linear equations. The theory relies on the bijection property of bipartite graph and rectangular Boolean matrix representation. The concept of perfect elimination matrices is extended from the classification under similarity transformations to that under equivalence transformations with permutation matrices. The reducibility problem is treated with a new and simpler proof than found in the literature. A number of useful algorithms are described. The minimum deficiency algorithms are extended to the new classification, where the latter required a different technique of proof. 13 figures, 7 tables