SOR.m

clc;
clear;
% Giving all inputs
n=input('\n Enter the numbr of equations: ');
A=input('\n Enter the entries of the coefficient matrix row-wise: ');
b=input('\n Enter the RHS given data of the system (as column vector) : ');
x=input('\n Enter the initial guess (as column vector): ');
m=input('\n Enter the maximum number of iteration: ');
w=input('\n Enter a value of the SOR Parameter: ');
y=zeros(n,1);
% Creating a matrix to store the results of each iteration
X=zeros(n,m+1);
% Storing the initial data in the first column of a matrix X
X(:,1)=x;
% Checking the necessary condition for the parameters w of SOR method to run the iteration
p=1;
while (p==1)
    if (w > 0) && (w < 2)
        p=0;
    else
        p=1;
        fprintf("\n SOR iteration will not converge for this given value of the parameter w,\n" + ...
        " please enter another value of w that lies in the interval (0,2). w = ");
        w=input('');
    end
end
if p==0
    % Checking the necessary condition on the diagonal elements of A to run the iteration
    v=0;
    for i=1:n
        if A(i,i)==0
            v=v+1;
            fprintf("SOR itereation can not be used. May need to do equations swapping. \n");
        end
    end
    if v==0
        % Starting the iteration
        for k=1:m
            for i=1:n
                u=0;
                for j=1:i-1
                    u=u+A(i,j)*y(j);
                end
                z=0;
                for j=i+1:n
                    z=z+A(i,j)*x(j);
                end
                y(i)=(1-w)*x(i)+(w/A(i,i))*(b(i)-u-z);
            end
            x=y;
            % Storing the results of each iteration in the matrix X
            X(:,k+1)=x;
        end
        % Printing the outputs
        fprintf("\n %d number of SOR iterations  are given as (columnwise):\n\n", m);
        % disp(X);
        % To get the output in 6 decimal places
        disp(cell2mat(compose('%10.6f',X)));
        fprintf("\n");
    end
end