Path: utzoo!attcan!uunet!van-bc!ubc-cs!fs1!ee.ubc.ca!jmorriso
From: jmorriso@ee.ubc.ca (John Paul Morrison)
Newsgroups: comp.sys.handhelds
Subject: Re: Interestring Property of HP-* Calculators
Keywords: 48SX,COS
Message-ID: <1990Oct25.145917@ee.ubc.ca>
Date: 25 Oct 90 21:59:17 GMT
References: <2821@uc.msc.umn.edu> <15610@mentor.cc.purdue.edu> <2830@uc.msc.umn.edu>
Sender: root@fs1.ee.ubc.ca
Reply-To: daveg@ee.ubc.ca
Organization: UBC Electical Engineering VLSI Lab
Lines: 21




I _do_ think this is about floating point precision.
the function you strated with was
	cos(pi/180*x)=x
then the inverse is
	180/pi*acos(x)=x

BOTH of these have fixed points, since a fixed point is where f(x)=x.
However the first fixed point is stable. ie if the fixed point is perterbed,
it will converge come back to that point after some more iterations.

The second fixed point is UNstable, ie an error will be quickly amplified.

This iterative technique is called Picard's method (at least in some
books) for 
finding roots. If you can write g(x)=o as f(x)=x, you can iteratively
find a root
of g(x). But if r is near the root of g(x), the series will converge if
|g'(r)| < 1.