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.

翻译：我们将文献[SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)]中针对矩阵函数近似Lanczos方法的误差界推广至块算法。数值实验表明，我们的误差界对块大小的变化具有较好的鲁棒性，并有望用作实用的停止准则。进一步实验旨在更好地理解如何选择特定超参数以最大化误差界的质量，即使在先前研究的块大小为一的情形下亦是如此。