Fixed-point iterative approach for solving linear Diophantine systems with bounds on the variables

Systems of linear Diophantine equations arise from several applications. Scholars have given attention to such systems and come up with several effective solutions. A new approach, called the fixed-point iterative method, was proposed to solve linear Diophantine equations with lower and upper bounds on the variables. Two steps are involved in solving this problem. First, the problem is transformed into a polytope judgment problem . Then, the approach is used to judge the existence of an integer point in the polytope. Compared with the branch-and-bound method, results show that the approach is feasible and effective for solving linear Diophantine systems.