The author introduces the definition of normal solution to a linear program, which is an exact solution with some least norm property if the linear program is solvable, otherwise an approximate solution with some least norm property also. By considering normal solutions we are led to (i) iterative successive overrelaxation (SOR) methods capable of solving very large linear programs; (ii) approximate solutions to poorly posed or unsolvable linear programs; (iii) a stable solution or approximate solution, to a linear program, endowed with a least norm property. The paper presents computational results on the comparison of one of the suggested SOR algorithms and the XMP revised simplex linear programming code (Marsten).