gauss siedel iteration solver with an inital node and a final node in matlab

The Gauss-Siedel method is a numerical iteration algorithm to solve systems of linear equations of the form Ax=b. It is an iterative method, meaning it starts from an initial guess and iteratively refines the guess to converge to the exact solution. Here is an implementation of the Gauss-Siedel method with an initial guess "x0" and a final guess "tol" in MATLAB:

main.m
function [ x, iter ] = gauss_siedel_solver( A, b, x0, tol )
% Solves Ax=b using the Gauss-Siedel iteration method
% Inputs:
%     A   - coefficient matrix
%     b   - constant vector
%     x0  - initial solution guess
%     tol - iterative tolerance
% Outputs:
%     x    - solution vector
%     iter - number of iterations performed

% matrix dimensions
n = size(A,1);

% initializations
x = x0;
iter = 0;
residual = Inf;

% perform Gauss-Siedel iteration
while residual > tol && iter < 1000
    x_old = x;
    for i = 1:n
        x(i) = (1/A(i,i)) * (b(i) - A(i,1:i-1)*x(1:i-1) - A(i,i+1:n)*x_old(i+1:n));
    end
    residual = norm(A*x-b)/norm(A*x_old-b);
    iter = iter + 1;
end

end
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Here, A is the coefficient matrix, b is the constant vector, x0 is the initial solution guess, and tol is the iterative tolerance. The function outputs the solution vector x and the number of iterations performed iter.

To use this function, simply call it with the appropriate input parameters:

main.m
A = [2 1; 1 3];
b = [3; 5];
x0 = [0; 0];
tol = 1e-6;

[x, iter] = gauss_siedel_solver(A, b, x0, tol);
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This will solve the system of equations Ax=b using the Gauss-Siedel method with an initial guess of x0 and an iterative tolerance of tol, and output the solution vector x and the number of iterations performed iter.