A posteriori error bounds for the block-Lanczos method for matrix function approximation

We extend the error bounds from Chen et al. (SIAM J. Matrix Anal. Appl 43(2):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 criterion. Further experiments work toward 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.