the loop is not converging it is giving me an infinite value(it is increasing)

clear variables
close all
clc


A = [1 1 2; 1 2 4; 1 2 5];
x = [1; 2; 3];
Error = 0.00001;

Diff= 1;

while Diff>Error
    
    x1=A*x;
    
    
    Diff=norm(x1-x);
    
    x=x1;
end

[Mahmoud Chawki]

still not working still not working the answer is infinity for x and NAN for Diff

Answer 1

[Torsten]

Why do you think your fixed-point iteration should converge ?

If the absolute values of the eigenvalues of A were all < 1, it would work. But it is not the case:

A = [1 1 2; 1 2 4; 1 2 5];
eig(A)

ans = 3×1

7.1842 0.5728 0.2430

[Mahmoud Chawki]

i did not understand you

what i am trying to do is tomultiply a matrix by a vector to get a new vector then use the new vector by multiplying it with the same matrix untill the vector stop changing (converges)

[Torsten]

Try A = 5. Take a vector x = 1. Then x1 = 5*1 = 5, x2 = 5*5 = 25,... No convergence.

Try A = 0.5. Take a vector x = 1. Then x1 = 0.5*1 = 0.5, x2 = 0.5*0.5=0.25,... Convergence.

What's the difference ? abs(A) < 1 ...

[Mahmoud Chawki]

how can i make it work?

[Torsten]

What do you mean by "make it work" ? It works as you have programmed it and gives you the correct result for the matrix A and the initial vector x: Divergence.

[Mahmoud Chawki]

i found the answer, i need to normalize the new vector before using it again. thank you