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Mathematics > Numerical Analysis

arXiv:2210.17107 (math)
[Submitted on 31 Oct 2022]

Title:An adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations

Authors:Pascal Heid
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Abstract:We will consider the damped Newton method for strongly monotone and Lipschitz continuous operator equations in a variational setting. We will provide a very accessible justification why the undamped Newton method performs better than its damped counterparts in a vicinity of a solution. Moreover, in the given setting, an adaptive step-size strategy will be presented, which guarantees the global convergence and favours an undamped update if admissible.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2210.17107 [math.NA]
  (or arXiv:2210.17107v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.17107
Related DOI: https://doi.org/10.1007/s00013-023-01858-x

Submission history

From: Pascal Heid [view email]
[v1] Mon, 31 Oct 2022 07:32:02 UTC (355 KB)
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