数值分析SOR迭代

function [X,Number_of_iteration] = SOR_iteration(A,B,P,delta,max1,W)
% Input  - A is an N x N nonsingular matrix
%        - B is an N x 1 matrix
%        - P is an N x 1 matrix: the initial guess
%        - delta is the tolerance for P
%        - max1 is the maximum number of iterations
%        - W is the relax factor
% Output - X is an N x 1 matrix: the SOR approximation to the 
%        - solution of the AX = B
N = length(B);
count = 0;
for k = 1 : max1
    for j = 1 : N
        if j == 1 
            X(1) = (1 - W) * P(1) - (B(1) - (A(1,(2:N)) * P(2:N))) / (A(1,1) / W);
        elseif j == N
            X(N) = (1 - W) * P(N) - (B(N) - (A(N,(1:N-1)) * X(1:N-1)')) / (A(N,N) / W);
        else
            %X contains the kth approxiamation and P the (k-1)st
            X(j) = (1 - W) * P(j) - (B(j) - A (j,1:j-1) * X(1,j-1)' - A(j,(j+1:N)) * P(j+1 : N)) / (A(j,j) / W);
        end
    end
    count = count + 1;
    err = abs(norm(X'-P));
    reletive_err = err/(norm(X)+eps);
    P = X';
        if(err < delta) || (reletive_err < delta)
            break
        end
end
X = X';
Number_of_iteration = count;