Jacobi iterative method in matlab

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.

Answer 1

[Mathieu NOE]

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

[Michelle]

Thx! Can I get x into 2 x i matrix?

[Mathieu NOE]

hello

sorry , I don't understand your question