论文标题
矩阵函数近似的块 - lanczos方法的后验误差界限
A posteriori error bounds for the block-Lanczos method for matrix function approximation
论文作者
论文摘要
我们从[Simax，vol。 43，ISS。 2，pp。787-811（2022）]对于lanczos方法，用于矩阵函数近似与块算法的近似。数值实验表明，我们的界限对于更换块大小的范围相当强大，并且有可能用作实际停止标准。进一步的实验可以更好地理解如何选择某些超参数，以最大程度地提高误差界限的质量，即使在先前研究的块大小中，也是如此。
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.
