We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)]
for the Lanczos method for matrix function approximation to the block
algorithm. Numerical experiments suggest that our bounds are fairly robust to
changing block size and have the potential for use as a practical stopping
criteria. Further experiments work towards a better understanding of how
certain hyperparameters should be chosen in order to maximize the quality of
the error bounds, even in the previously studied block-size one case