How accurate does Newton have to be?
Abstract
We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. We briefly discuss implications for parallel solvers.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2023
- DOI:
- 10.48550/arXiv.2303.17911
- arXiv:
- arXiv:2303.17911
- Bibcode:
- 2023arXiv230317911K
- Keywords:
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- Mathematics - Numerical Analysis;
- 65H10;
- G.1.5
- E-Print:
- 12 pages, 2 figures, preprint accepted by PPAM 2022, expected to appear in LNCS vol. 13826 during 2023