Relative convergence of the solution of a doubly infinite set of equations

The p ap er deals with t he relative convergence of a d oubly-i nfini te set of equations p ertaining to a boundary value problem in a waveguide.It is shown th at the solution for t he equations converges differently for different cho ices of the co mbination of t h e n umber of equations from t h e t wo sets.This is demonstrated by st ud ying t h e co nvergence prop er ties of t h e truncated set of equation s as t he nu mber of equations is m ade ind efini t ely largc.It is proven t hat t he solution for th e reflection coeffi cie nt becom cs id entical with t h e exact solu t ion only wit h a p ar ticular choice of th e ratio of t he eq uations.Thi s choice of t h c unique ra t io is also sh own to be consistent with t h e edge con di tion.