An algorithm to solve Hilbert systems of linear equations precisely

摘要

This paper presents an error-free form of Levison's algorithm to solve a rational general Hilbert system of linear equations. It removes roundoff errors. Their accumulation, if using classic algorithms, can destroy the result. The algorithm employs modular arithmetic. The number of necessary operations in one modulo class is proportional to N2. The method is well suited for implementation in parallel computers.