Before revision:  Numerical experiments on large matrix pencils illustrate the method. As compared to previous methods, the new method is found to be more robust and efficient and is conjectured by experiment results to be more efficient in parallelized settings.
After revision:  Numerical experiments on large matrix pencils illustrate this method. The new method is found to be more robust and efficient and is conjectured by experiment results to be more efficient in parallelized settings.