I am trying to write a program using the inverse iteration method and I am running across an issue. With each iteration my values are not changing. With each iteration x(i) should become xnorm(i) and rho(i) should equal rho(i+1). I suspect that this is the problem, that somehow the order of the operations regarding rho is making it so that the relative error doesn't change. I have tried taking rho(i) out of the loop and calculating rho(1) but that did not seem to help either. I've been struggling with these problems for a few days so the help is really appreciated.
%Declare initial variables
A = [2 1;1 4];
b = [1;1];
B = [1 0;0 1];
Nmax = 20;
TOL = 1*10^5;
k = 1;
x = zeros(2,21);
x_a = zeros(21,2);
rho = zeros(21,1);
xnorm = zeros(2,21);
x(:,1) = A\b;
x_a(1,:) = x(:,1)';
for i =1:Nmax
%Calculate old values
rho(i) = (x_a(i,:)*A*x(:,i))/(x_a(i,:)*B*x(:,i))
%Calculate new values
xnorm(:,i) = (1/sqrt(x_a(i,:)*B*x(:,i)))*x(:,i)
rho(i+1) = (x_a(i,:)*A*x(:,i))/(x_a(i,:)*B*x(:,i))
%Check for convergence
relative_error = abs((rho(i+1)rho(i))/rho(i+1))
if ( relative_error ~= 0 && relative_error <= TOL )
x(:,i+1) = xnorm(:,i)
rho(i+1) = rho(i+1)
k = k
return
elseif (relative_error == 0)
x(:,i) = xnorm(:,i)
rho(i) = rho(i+1)
k = k+1
elseif (relative_error > TOL)
x(:,i) = xnorm(:,i)
rho(i) = rho(i+1)
k = k+1
end
end
