NavList:

Folks, I believe Mike is expressing a sentiment that is probably felt by other readers of this thread. They hear angels dancing...

Does this question about iteration convergence matter? Yes, if you're into such things, it matters to you, and there's nothing wrong with that. And with certainty, there are many cases that do not converge. Does this matter in practice?? No. First, it never comes up except in "textbook" or "gaming" scenarios. No real navigator is ever that lost in the modern world. And if it does come up in a textbook case or a game or similar challenge, there's a valid alternative that always works: draw it on a spheroid (a rubber ball, an orange, a canteloupe, a deformed watermelon, or other suitable round thing!). Drawing the circles of position on a sphere is a direct, analog, implementation of the fundamental principle of the celestial position fix by altitude observations so everyone should try that at least once. 

Frank Reed