High-index saddle dynamics provides an effective means to compute the any-index saddle points and construct the solution landscape. In this paper we prove the optimal-order error estimates for Euler discretization of high-index saddle dynamics with respect to the time step size, which remains untreated in the literature. We overcome the main difficulties that lie in the strong nonlinearity of the saddle dynamics and the orthonormalization procedure in the numerical scheme that is uncommon in standard discretization of differential equations. The derived methods are further extended to study the generalized high-index saddle dynamics for non-gradient systems and provide theoretical support for the accuracy of numerical implementations.

翻译：高指数马鞍动态提供了计算任何指数马鞍点和构建解决方案景观的有效手段。 在本文件中,我们证明,在时间级大小方面,高指数马鞍动态的Euler离散估计是最佳的顺序错误,文献中仍未处理。我们克服了主要困难,这些困难在于马鞍动态的强非线性以及不同方程标准离散中不常见的数字图中的正正统化程序。衍生方法进一步扩展,以研究非梯度系统通用的高指数马鞍动态,并为数字执行的准确性提供理论支持。