I am trying to write a program that utilizes the inverse iterative method. I calculate an initial x value and rho value given the matrices A, B, and b. I calculate a value of x normalized to the matrix B (xnorm) as well as a new value for rho for each iteration. Given that the relative error of rho is less than my preset tolerance (TOL) the loop ends, otherwise xnorm becomes the new value for x and the rho(i+1) becomes rho(i). The problem is in calculating rho(i), I am told my matrix dimensions do not agree when I have checked the sizes multiple times. Any suggestions? Thanks.
%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 && relative > TOL) x(i+1) = xnorm(i) rho(i) = rho(i+1) k = k+1