Obtained true when false

I am trying to implement the Jacobi (j) and Gauss-Seidel (gs) method on Matlab. In order to those methods to work I need to check the norms of their matrices Cj and Cgs, and if they are greater than 1 there's the need of the evaluation of the spectral radius:

rj = [norm(Cj,1) norm(Cj,2) norm(Cj,"inf") max(abs(eig(Cj)))];
rgs = [norm(Cgs,1) norm(Cgs,2) norm(Cgs,"inf") max(abs(eig(Cgs)))];

then I check if any of those is less than 1:

for i=1:4
    if rj(i)<1 && rgs(i)<1 %if they both work, prefer gs
        [x,k]=Gauss_Seidel(A,b,kmax,tol);
        break;
    elseif rgs(i)<1
        [x,k]=Gauss_Seidel(A,b,kmax,tol);
        break;
    elseif rj(i)<1
        [x,k]=Jacobi(A,b,kmax,tol);
        break;

the point is that I get these two arrays for rj and rgs and theese answers for the check:

why the last component is considered to be lesser than 1?

Answer 1

[Torsten]

In the output, the number is rounded to 1.00000... . But this does not mean that the original number cannot be < 1.