mirror of
https://github.com/kuhyx/WUT_Computer_Science.git
synced 2026-11-13 05:10:54 +01:00
41 lines
1.2 KiB
Matlab
41 lines
1.2 KiB
Matlab
function [x step] = GaussSeidel(A, b, x0, tol, max_iter)
|
|
% use this algorithm only if it converges
|
|
N = tril(A);
|
|
P = N - A;
|
|
Ggs = inv(N) * P;
|
|
% calculate the spectral radius of Ggs
|
|
sr = max(abs(eig(Ggs)));
|
|
% check if the algorithm converges
|
|
if (sr - 1) >= eps
|
|
x = NaN;
|
|
step = -1;
|
|
disp('Matrix does not converge');
|
|
return;
|
|
endif
|
|
|
|
n = length(b);
|
|
x = x0;
|
|
% iterate to the maximum number of iterations
|
|
for step = 1 : max_iter
|
|
% iterate through every x(i)
|
|
for i = 1 : n
|
|
% compute the sum using the updated values from the current step
|
|
new_values_sum = A(i, 1 : i - 1) * x(1 : i - 1);
|
|
|
|
% compute the sum using the previous step values
|
|
old_values_sum = A(i, i + 1 : n) * x0(i + 1 : n);
|
|
|
|
x(i) = b(i) - (old_values_sum + new_values_sum);
|
|
x(i) = x(i) / A(i, i);
|
|
endfor
|
|
|
|
% when the new values get close enough to the last values
|
|
% regarding the imposed tolerance "tol", we reached the solution
|
|
if norm(x - x0) < tol
|
|
break;
|
|
endif
|
|
% update the last computed values with the new values
|
|
x0 = x;
|
|
endfor
|
|
endfunction
|