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

11/28/2022

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by   Qichen Xu, et al.

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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. Further experiments work towards a better understanding of how certain hyperparameters should be chosen in order to maximize the quality of the error bounds.