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Fixed Point Iteration Algorithm with Graphs #91

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e2c95c4
Create fixedpoint_iter
hamzahs1 Jan 23, 2023
4dadc46
Rename fixedpoint_iter to fixed_point_iter
hamzahs1 Jan 23, 2023
c6fd72b
Update fixed_point_iter
hamzahs1 Jan 23, 2023
af1ca0c
Added .m extension for MATLAB
hamzahs1 Jan 23, 2023
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29 changes: 29 additions & 0 deletions algorithms/arithmetic_analysis/fixed_point_iter.m
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Original file line number Diff line number Diff line change
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function fpi(f,a, b, x0, N)

% generate the cobweb diagram associated with
% the iteration: x_{n+1}=f(x_n).
% N is the number of iterates, and
% (a,b) is the interval
% x0 is the initial point.
% plot y=f(x)

x=a:.01:b;
y=f(x);
figure
hold on;
title('fixed point iteration')
plot(x,y,'k'); % plot the function
plot(x,x,'r'); % plot straight line
x(1)=x0; % plot orbit starting at x0
for i=1:N
x(i+1)=f(x(i));
if i==1
line([x(i),x(i)],[0,x(i+1)]);
else
line([x(i),x(i)],[x(i),x(i+1)]);
end
pause
line([x(i),x(i+1)],[x(i+1),x(i+1)]);
pause
end
hold off;