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Mathematics > Numerical Analysis

arXiv:2211.15643 (math)
[Submitted on 28 Nov 2022 (v1), last revised 14 Apr 2024 (this version, v4)]

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

Authors:Qichen Xu, Tyler Chen
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65G99 (Primary), 15A15 (Secondary)
ACM classes: G.1.3
Cite as: arXiv:2211.15643 [math.NA]
  (or arXiv:2211.15643v4 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.15643
Related DOI: https://doi.org/10.1007/s11075-024-01819-7

Submission history

From: Qichen Xu [view email]
[v1] Mon, 28 Nov 2022 18:50:43 UTC (1,075 KB)
[v2] Tue, 11 Apr 2023 17:49:28 UTC (1,753 KB)
[v3] Mon, 4 Sep 2023 13:59:39 UTC (1,754 KB)
[v4] Sun, 14 Apr 2024 23:02:25 UTC (4,041 KB)
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