Convergence Analysis of Discrete High-Index Saddle Dynamics
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Publication:5043630
DOI10.1137/22M1487965zbMATH Open1506.37101arXiv2204.00171MaRDI QIDQ5043630
Author name not available (Why is that?)
Publication date: 6 October 2022
Published in: (Search for Journal in Brave)
Abstract: Saddle dynamics is a time continuous dynamics to efficiently compute the any-index saddle points and construct the solution landscape. In practice, the saddle dynamics needs to be discretized for numerical computations, while the corresponding numerical analysis are rarely studied in the literature, especially for the high-index cases. In this paper we propose the convergence analysis of discrete high-index saddle dynamics. To be specific, we prove the local linear convergence rates of numerical schemes of high-index saddle dynamics, which indicates that the local curvature in the neighborhood of the saddle point and the accuracy of computing the eigenfunctions are main factors that affect the convergence of discrete saddle dynamics. The proved results serve as compensations for the convergence analysis of high-index saddle dynamics and are substantiated by numerical experiments.
Full work available at URL: https://arxiv.org/abs/2204.00171
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