طرح و تحليل الگوريتم هاي جديد براي حل برخي دستگاه ها و برنامه ريزي خطي روي فضاهاي حقيقي و صحيح

First a new approach, based on ABS methods, is presented for computing the general solution of real linear inequality systems having full row rank, and then the results are used to solve linear programming problems with full row rank linear intequality constraints. The approach determines whether the problem is unbounded or computes the general solution (if it exists). Then this approach is adapted to solve linear integer ineguality systems. Using the results obtained, it is shown how to transform an integer linear programming problem with full row rank inequality constraints to a problem having finitely many integer solutions, and subsequently how to obtain one solution. Finally, a new class of algorithms ,based on the ABS methods, is presented for solving linear equations so that in every iteration two new equations are satisfied. Numerical results obtained from testing the implementation of certain special versions of the proposed algorithms indicate the efficiency of the new algorithms and the precision of the computed solutions.