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[SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)]中关于Lanczos方法矩阵函数逼近的误差界推广到块算法。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，并具有作为实用停止准则的潜力。进一步的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质量，即使是在之前研究过的块大小为一的情形下也是如此。