The exact analysis of sparse rectangular linear systems
Peter Alfeld, David J. Eyre · ACM Transactions on Mathematical Software · 1991
We describe the theory underlying the FORTRAN software package Goliath and give examples illustrating Its performance.Given a large, sparse, possibly rank-deficient, linear system with rational coefficients, Goliath provides the following information based on exact arithmetic: row dependencies, rank of the matrix, basis of the null space and solution of linear systems.