Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics Article Swipe
Lei Zhang
,
Pingwen Zhang
,
Xiangcheng Zheng
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.01012
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.01012
We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere. Due to the semi-implicit treatment and the novel computational procedure, the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations, and the computations of the state variable and directional vectors are coupled with the retraction, the vector transport and the orthonormalization procedure, which significantly complicates the analysis. We address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2307.01012
- https://arxiv.org/pdf/2307.01012
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4383180379
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- OpenAlex ID
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https://openalex.org/W4383180379Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2307.01012Digital Object Identifier
- Title
-
Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamicsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-07-03Full publication date if available
- Authors
-
Lei Zhang, Pingwen Zhang, Xiangcheng ZhengList of authors in order
- Landing page
-
https://arxiv.org/abs/2307.01012Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2307.01012Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2307.01012Direct OA link when available
- Concepts
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Orthonormality, Saddle point, Computation, Applied mathematics, Mathematics, Saddle, Computer science, Scheme (mathematics), Variable (mathematics), Mathematical optimization, Algorithm, Mathematical analysis, Geometry, Orthonormal basis, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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