Quasihomogeneous Infinite Systems of Linear Algebraic Equations

Abstract

The broad practical application of an infinite systems of linear algebraic equation is greatly limited by the insufficient development of the theory of these systems. In particular, the question about uniqueness of infinite systems solutions remains open. This is because that solving a corresponding homogeneous system is much more difficult task than solving an inhomogeneous system. The solving a homogeneous infinite systems is connected with the study of special infinite systems the so-called quasihomogeneous systems. Such systems are found, for example, in the theory of electrical circuits. An infinite system of linear algebraic equations is quasihomogeneous, if the finite amount of numbers on the right-hand side are not equal to zero, and the infinite amount of them are equal to zero. In this paper, we develop a numerical algorithm for finding the solution of quasihomogeneous infinite systems. In particular, it has been shown that such systems can behave both as “purely” inhomogeneous, and as almost homogeneous systems, it depends on coefficients of the system.