  In this paper we consider the computation of H-infinity norm of retarded
time-delay systems with discrete pointwise state delays. It is well known that
in the finite dimensional case H-infinity norm of a system is computed using
the connection between the singular values of the transfer function and the
imaginary axis eigenvalues of an Hamiltonian matrix. We show a similar
connection between the singular values of a transfer function of a time-delay
system and the imaginary axis eigenvalues of an infinite dimensional operator
$\mathcal{L}_{\xi}$. Using spectral methods, this linear operator is
approximated with a matrix. The approximate H-infinity norm of the time-delay
system is calculated using the connection between the imaginary eigenvalues of
this matrix and the singular values of a finite dimensional approximation of
the time-delay system. Finally the approximate results are corrected by solving
a set of equations which are obtained from the reformulation of the eigenvalue
problem for $\mathcal{L}_{\xi}$ as a finite dimensional nonlinear eigenvalue
problem.
