% It is a variant of Gauss-Seidel Method resulting in faster convergence.

clc; clear all;

disp('For `Ax=B` system of equations.')

A = input('Matrix A : ');

B = input('Matrix B : ');

x0 = input('Initial guess x0 : ');

w = input('Relaxation factor (> 1) : ');

tolerance = input('Tolerance required : ');

maxIte = input('Maximum Iterations : ');

if size(B,1) ~= size(A,1) || size(x0,1) ~= size(A,1)

disp('Invalid Inputs B and/or x0, please provide as `nx1` matrix.')

N = size(A,1);

ite = 1;

x=zeros(size(x0));

gotSoln=false;

while ite <= maxIte

for row = 1:N

x(row) = (1-w)*x0(row) + w*(B(row) - A(row,1:row-1)*x(1:row-1) - A(row,row+1:N)*x0(row+1:N))/A(row,row);

end

if abs(x-x0) < tolerance

gotSoln=true;

fprintf('\nConverged, Solution of system is :');

x

fprintf('Iterations Required : %d\n',ite);

break;

else

ite = ite + 1;

x0 = x;

end

end

if ~gotSoln

fprintf('\nDid not converge.')

disp('Possible reasons include -')

disp('Matrix A is')

disp('neither `strictly or irreducibly diagonally dominant`')

disp('nor `symmetric positive-definite` (keep 0 < w < 2)')

disp('The standard convergence condition (for any iterative method) -')

disp('Spectral radius of the iteration matrix should be less than 1.')