Infinite systems of equations. The effect of truncation

Abstract

This work addresses an infinite system of equations. There are infinite systems for which the form of the asymptotic expansion of the components {XM} of the infinite-dimensional solution vector x can readily be found for large suffixes M. It is shown that for such systems, this expansion for XM can be used to improve the bound for Δ(M), and in suitable cases to find the form of an asymptotic expression for Δ(N), through not necessarily the explicit coefficients. The theory is illustrated using an example. The methods used are elementary, involving at most Schwarz's Inequality.