Generalization of the Gauss-Jordan Method for Solving Homogeneous Infinite Systems of Linear Algebraic Equations

In this paper, first, using reduction in a narrow sense (the simple reduction method), we have generalized the classical Gauss-Jordan method for solving finite systems of linear algebraic equations to inhomogeneous infinite systems. The generalization is based on a new theory of solving inhomogeneous infinite systems proposed by us, which gives an exact analytical solution in the form of a series. Second, we have shown that the use of reduction in the narrow sense in the case of homogeneous systems provides only a trivial solution. Therefore, to generalize the Gauss-Jordan method for solving infinite homogeneous systems we use the reduction method in a wide sense. A numerical comparison showing acceptable accuracy is presented.