write a system of linear equations using gauss sidel interation solver in matlab

To write a system of linear equations using Gauss-Sidel iteration solver in MATLAB, you need to follow these steps:

1. Define the coefficient matrix A, right-hand side vector b, and initial guess x.

main.m
A = [2 -1 0; -1 2 -1; 0 -1 2];
b = [1; 0; 1];
x0 = [0; 0; 0];
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2. Create a loop that performs Gauss-Sidel iteration. Repeat until convergence, where the norm of the error is less than a specified tolerance (tol).

main.m
maxiter = 1000;
tol = 1e-6;

x = x0;
for k = 1:maxiter
    for i = 1:size(A,1)
        x(i) = (b(i) - A(i,1:i-1)*x(1:i-1) - A(i,i+1:end)*x(i+1:end)) / A(i,i);
    end
    if norm(x - x0, inf) < tol
        break;
    end
    x0 = x;
end
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3. Output the solution x.

main.m
disp(x);
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By running this code, you will get the solution of the system of linear equations.