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.
Bibliographical noteFunding 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 (email@example.com). ‡School of Mathematics, University of Minnesota, Minneapolis, MN, 55455 (firstname.lastname@example.org).
- Minimum energy path
- String method