  We reformulate the Lanczos tau method for the discretization of time-delay
systems in terms of a pencil of operators, allowing for new insights into this
approach. As a first main result, we show that, for the choice of a shifted
Legendre basis, this method is equivalent to Pad\'e approximation in the
frequency domain. We illustrate that Lanczos tau methods straightforwardly give
rise to sparse, self nesting discretizations. Equivalence is also demonstrated
with pseudospectral collocation, where the non-zero collocation points are
chosen as the zeroes of orthogonal polynomials. The importance of such a choice
manifests itself in the approximation of the $H^2$-norm, where, under mild
conditions, super-geometric convergence is observed and, for a special case,
super convergence is proved; both significantly faster than the algebraic
convergence reported in previous work.
