Solving Very Sparse Rational Systems of Equations
William J. Cook, Daniel E. Steffy · ACM Transactions on Mathematical Software · 2011
Efficient methods for solving linear-programming problems in exact precision rely on the solution of sparse systems of linear equations over the rational numbers. We consider a test set of instances arising from exact-precision linear programming and use this test set to compare the performance of several techniques designed for symbolic sparse linear-system solving. We compare a direct exact solver based on LU factorization, Wiedemann’s method for black-box linear algebra, Dixon’s p -adic-lifting algorithm, and the use of iterative numerical methods and rational reconstruction as developed by Wan.