Software method for solving systems of linear equations having integer variables

摘要

This invention describes a software method for computers for solving integer programming problems containing systems of linear equations where part of or all of the variables may take only integer values. Said software method consists of 4 main steps. First, all of or part of said system is transformed into a regularized system. In a second step, the regularized system is further transformed into an ordered system. In a third step, the regularized and ordered system is further transformed into a non-interfering system. In a last step, solutions to said system are determined by finding solutions which are common to all equations of said system. This is done by using a successive and recursive approximation algorithm. Finally, prior to executing said 4 steps, said system may have to be conditioned such every variable-coefficient of the system is non-zero.