  We present a two-stage algorithm for the parallel reduction of a pencil to
Hessenberg-triangular form. Traditionally, two-stage Hessenberg-triangular
reduction algorithms achieve high performance in the first stage, but struggle
to achieve high performance in the second stage. Our algorithm extends
techniques described by Karlsson et al. to also achieve high performance in the
second stage. Experiments in a shared memory environment demonstrate that the
algorithm can outperform state-of-the-art implementations.
