Abstract
We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 873-898 |
| Number of pages | 26 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 17 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Funding Information:∗Received by the editors July 17, 2018; accepted for publication (in revised form) May 14, 2019; published electronically June 27, 2019. http://www.siam.org/journals/mms/17-2/M120103.html Funding: The first author was supported by the NSF RTG: Computational and Applied Mathematics in Statistical Science, award number 1547396. The second author was partly supported by the U.S. Department of Energy Office of Science, grant DE-SC0012733, and the Simons Foundation. †University of Massachusetts, Amherst, MA, 01003-9305 (bvankoten@gmail.com). ‡School of Mathematics, University of Minnesota, Minneapolis, MN, 55455 (luskin@umn.edu).
Funding Information:
The first author was supported by the NSF RTG: Computational and Applied Mathematics in Statistical Science, award number 1547396. The second author was partly supported by the U.S. Department of Energy Office of Science, grant DE-SC0012733, and the Simons Foundation.
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics
Keywords
- Convergence
- Minimum energy path
- Stability
- String method