% CLASS27SEPT.TXT   Commands I used in class on Monday,
% regarding fixed point iteration of some simple functions.
%
% Suggestion:  Cut and paste these to the command line.
%   You can run this as a program (i.e. save as .m), but
%   it does not produce nice output; it spews lots of numbers.

% manually do fixed point iteration for  g(x) = cos(x):
p = 100*randn(1)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)
p=cos(p)

% continue by automating it:
format long
for j=1:30, p=cos(p), end

% similar for  g(x) = sin(x)  and  g(x) = tan(x):

p=116.52,  for j=1:30000, p=sin(p), end  % slow convergence to zero

p=116.52,  for j=1:30000, p=tan(p), end  % rather unpredictable