I have made following matlab code for computing the Moore-Penrose inverse of a given matrix A.
A = randn(100) % given matrix
beta = 1/norm(A,2)^2
x0 = beta.*A' % initial approximation, A' is the transpose of matrix A
k = 0;
iter = 0
f = 1 ;
I = eye(100);
while (f > 1.0e-007)
x1 = 2*x0 - x0*A*x0; % x1 is approximation of Moore-Penrose inverse of matrix A
iter = iter+1
a = norm(A*x1*A-A, 2); % error norm
b = norm(x1*A*x1 - x1);` % error norm
c = norm ((A*x1)' - A*x1, 2 ); % error norm
d = norm ((x1*A)' - x1 *A, 2); % error norm
B = [a, b, c, d];
f = max(B);
x0 = x1;
end
Since matrix A is changing after every iterations hence values of a,b ,c and d are also changing. I am trying to compute average of values a, b, c and d after hundred repetitions but I am unable to do so. Could anybody help me? I would be very much thankful to you.