The use of a permutation in the solution of a system of simultaneous linear equations

Abstract

In the Gauss and Gauss-Jordan Reduction Methods for the solution of a system of simultaneous linear equations, A*X = B, the positioning for size in the ijp th pass is usually restricted to the elements:{ai,ijp | ijp≤i≤n}of the array A. In this paper, the positioning for size in the ijp th pass uses the elements:{ai,j | ijp≤i,j≤n}of the array A. Hence, columns, as well as rows, are exchanged in the array A.To minimize the complexity of the algorithm, additional structure is developed in the algorithm through the use of a permutation array.The algorithm allows for the study of singular systems of simultaneous linear equations.