  Parallel-in-time integration has been the focus of intensive research efforts
over the past two decades due to the advent of massively parallel computer
architectures and the scaling limits of purely spatial parallelization. Various
iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal,
PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been
described using different notations, and the convergence estimates that are
available are difficult to compare. We describe Parareal, PFASST, MGRIT and
STMG for the Dahlquist model problem using a common notation and give precise
convergence estimates using generating functions. This allows us, for the first
time, to directly compare their convergence. We prove that all four methods
eventually converge super-linearly, and also compare them numerically. The
generating function framework provides further opportunities to explore and
analyze existing and new methods.
