Solving Very Sparse Rational Systems of Equations
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 01, 2011
- Source ID
- 10.1145/1916461.1916463
Entities
People
- Daniel E. Steffy
- William Cook
Organizations
- Division of Civil, Mechanical & Manufacturing Innovation
- Georgia Tech
- Office of Naval Research