Eigenvalue degeneracy in real physical systems

[A. Neumaier]

numerical methods often do not meet the specifications.

This just means that the specifications are overly strict.

Typically, the input of a matrix problem is already inaccurate, hence requiring the output to be accurate to the last bit is meaningless. If $A$ is a Hermitian matrix with a double eigenvalue and you perturb each coefficient by $O(\epsilon)$, the eigenvalues will typically separate by an amount of $O(\sqrt{\epsilon})$ and the eigenvectors will typically even depend discontinuously on the perturbation. Thus the solution of the exact problem means nothing for the intended unknown problem nearby.

Since we didn't get closer after 175 posts I'll stop contributing to this thread.

 

[ErikZorkin]

Who didn't get closer? I did (as I mentioned some posts ago).