%%Fixed point Iteration animation result code
%Dejen Ketema  March, 2019
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%% Convergence Example1  x = cos(x)
%  fprintf('\ng(x) = cos(x)\n\n')
%  g=@(x) cos(x);
%   fixed_point_plot_2019(g,2,0,1000)(g,1,0,1.3);
%% Example 2
%f(x) = sin(x) - exp(-x); %using fixed-point iteration
fprintf('\ng(x) = x - (sin(x) - exp(-x))\n\n')
g=@(x) x-(sin(x)-exp(-x));
fixed_point_plot_2019(g,1,0,1.3);
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%% 2 Diverengence Example  x = arccos(x) does not converge
%  fprintf('\ng(x) = arccos(x)\n\n')
%  g=@(x) acos(x);
%  fixed_point_plot_2019(g,0.75,0,1.5);
%% Example 4 Diveregence 
%  fprintf('\ng(x) = x - 2 * (sin(x) - exp(-x))\n\n')
%  g=@(x) x-2*(sin(x)-exp(-x));
%  fixed_point_plot_2019(g,0.6,0,2); 
%% Converge fast
% fprintf('\ng(x) = x - 0.5 * (sin(x) - exp(-x))\n\n')
% g=@(x) x-0.5*(sin(x)-exp(-x));
%  fixed_point_plot_2019(g,1,0,1.3);
%%  g(x) = x - f(x)/f'(x) converges fundamentally faster (Newton's method)
% fprintf('\ng(x) = x - (sin(x) - exp(-x)) / (cos(x) + exp(-x))\n\n')
% g=@(x) x-(sin(x)-exp(-x))./(cos(x)+exp(-x));
%  fixed_point_plot_2019(g,1,0,1.3);