A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Hakel
Date: 2020 Jan 24, 19:39 -0800
Bill Lionheart wrote:
“Right. What I have in mind is to prove a result that says "if you are
within some specific distance of the correct position th iteration
converges", and I think it is pretty clear it can fail if you are far
enough away. As I said it is pretty much Newton's method on a sphere,
and there are plenty of general results about convergence of that.”
The following outline comes to my mind:
1) Quantify how much the adopted procedure starting from some AP brings you closer to the correct position after one pass.
2) Apply the Banach fixed-point theorem.