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Jacobi iterative method in matlab

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Michelle
Michelle on 20 May 2021
Commented: Mathieu NOE on 25 May 2021
When A = [ 10 5 ; 2 9 ] and y = [ 6 ; 3 ] and [A][x] = [y], solve x.
start with x1(0) = 0, x2(0) = 0 and continue until abs((x(i+1)-x(i))/x(i)) < e (e = 10^-4)
My code is
clear;
clc;
%%Input
A = [ 10 5 ; 2 9 ];
y = [ 6 ; 3 ];
x = zeros(size(y))
e = 0.0001;
%%Jacobi
D = [ 10 0 ; 0 9 ];
M = inv(D)*(D-A)
x_new = x;
if abs((x_new-x)/x) >= e
x_new = M*x_new + inv(D)*y
end
and it's error says 랭크 부족, rank = 0, tol = 0.000000e+00.

Accepted Answer

Mathieu NOE
Mathieu NOE on 21 May 2021
hello
there were quite a few bugs there - now see the correction below
you should do a while and not a for loop if you stop criteria is based on a error
inside the loop , the update logic was wrong and incomplete
also fixed a few initialization issues
clear;
clc;
%%Input
A = [ 10 5 ; 2 9 ];
y = [ 6 ; 3 ];
x = zeros(size(y));
e = 0.0001;
%%Jacobi
% D = [ 10 0 ; 0 9 ];
D = diag(diag(A));
invD = inv(D);
M = invD*(D-A);
x_new = x;
err = 1; % put a value here greater than e otherwise the while loop will not start
while err >= e
x_new = M*x + inv(D)*y; % update x_new
err = norm((x_new-x)./(x+eps)) % compute error (sue norm)
x = x_new; % update x based on x_new
end
x
  2 Comments
Mathieu NOE
Mathieu NOE on 25 May 2021
hello
sorry , I don't understand your question

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