```Date: Oct 20, 2011 12:43 PM
Author: Halley
Subject: For loop iterations not changing

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 variablesA = [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 valuesrho(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 convergencerelative_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 = kreturnelseif (relative_error == 0) x(:,i) = xnorm(:,i)rho(i) = rho(i+1)k = k+1elseif (relative_error > TOL)x(:,i) = xnorm(:,i)rho(i) = rho(i+1)k = k+1   end    end
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