simple Fixed Point Iteration

clear all;

clc;

x(1)=0;

g=@(x) exp(-x);

f=@(x) exp(-x)-x;

true_root=0.56714329;

disp('----------------------------------------------------');

disp('i xi Ea(%) Et(%) ');

disp('----------------------------------------------------');

for i=1:10

x(i+1)=g(x(i));

end

if x~=0

ea=100*abs(x(i+1)-g(x(i))/x(i+1));

end

e_t=100*abs(x-true_root)/true_root;

res=[[0:10]' x' ea' e_t'];

fprintf('%d %1.6f %3.3f %3.3f\n', res');

i want to add the ea. but i can. how can i this??

Answer 1

[Alan Stevens]

Probably more like this (though you don't seem to have used function f anywhere):

n = 11;
x = zeros(1,numel(n));
ea = zeros(1,numel(n));
g=@(x) exp(-x);
f=@(x) exp(-x)-x;
true_root=0.56714329;
disp('----------------------------------------');

----------------------------------------

disp('i       xi        Ea(%)       Et(%)     ');

i       xi        Ea(%)       Et(%)     

disp('----------------------------------------');

----------------------------------------

for i=1:n-1
    x(i+1)=g(x(i));

    if x(i+1)~= 0
        ea(i+1) = 100*abs(x(i+1)-x(i))/x(i+1);
    end
    
end
e_t = 100*abs(x-true_root)/true_root;
res=[(0:n-1)' x' ea' e_t'];
fprintf('%d %10.6f %10.3f %10.3f\n', res');

0   0.000000      0.000    100.000
1   1.000000    100.000     76.322
2   0.367879    171.828     35.135
3   0.692201     46.854     22.050
4   0.500474     38.309     11.755
5   0.606244     17.447      6.894
6   0.545396     11.157      3.835
7   0.579612      5.903      2.199
8   0.560115      3.481      1.239
9   0.571143      1.931      0.705
10   0.564879      1.109      0.399

[지민 이]

Thank you!!