gaussseidel.m

The Gauss鈥揝eidel method is a technique used to solve a linear system of equations.

function x=GaussSeidel(A,b,es)
%A=coefficient matrix
%b=right hand side vector
%es=stop critartion 
%maxit=max iterations 
%output:
%x=solution vector
maxit=100;
lambda=0.5; %underrelaxation parameter
if nargin<3, es=0.00001;end
[m n]=size(A);
if m~=n, error('matrix A must be square');end
C=A;
for i=1:n
    C(i,i)=0;
    x(i)=0;
end
x=x';
for i=1:n
    C(i,1:n)=C(i,1:n)/A(i,i);
end
for i=1:n
    d(i)=b(i)/A(i,i);
end
iter=0;
while (1)
    xold=x;
    for i=1:n
        x(i)=d(i)-C(i,:)*x;
         x(i) = lambda*x(i)+(1-lambda)*xold(i);
        if x(i)~=0
            ea(i)=abs((x(i)-xold(i))/x(i))* 100;
        end
    end
    iter=iter+1;
    if max(ea)<=es|iter>=maxit,break,end

end