n=63;

 T=2*eye(n)-diag(ones(1,n-1),1)-diag(ones(1,n-1),-1);

%b=sin([1:n]*2*pi/n)';

%b=rand(n,1)-0.5;
b=zeros(n,1);
b(fix(n/3))=-1;
b(fix(n/3)+1)=1;
b(fix(2*n/3))=1;
b(fix(2*n/3+1))=-1;

sol=T\b;

[U,S,V]=svd(T);

clf;
w=1; z=sort(eig(eye(n)-w*T/2)); plot(z(n:-1:1)); hold on
w=1/2; z=sort(eig(eye(n)-w*T/2)); plot(z(n:-1:1),'r'); 
w=2/3; z=sort(eig(eye(n)-w*T/2)); plot(z(n:-1:1),'g');
legend('w=1','w=1/2','w=2/3'); pause; hold off;



w=2/3;
R=eye(n)-w*T/2;
c=w*b/2;

V=V(:,n:-1:1);

x=zeros(n,1);
x=rand(n,1);

for i=1:3000
  e=sol-x;
  x=R*x+c;
  subplot(121);
  semilogy(abs(V'*e));
  axis([0 n 10^(-15) 10^5]);
  subplot(122);
  plot(sol,'r'); hold on;
  plot(e,'g'); 
  plot(x,'b');
  legend('solution','error','x');
  hold off
  pause
end