Error Estimate for Semi-implicit Method of Sphere-Constrained High-Index Saddle Dynamics  

作　　者：Lei ZHANG Pingwen ZHANG Xiangcheng ZHENG 

机构地区：[1]Beijing International Center for Mathematical Research,Center for Machine Learning Research,Centerfor Quantitative Biology,Peking University,Beijing 100871,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [3]School of MathematicalSciences,Laboratory of Mathematics and Applied Mathematics,Peking University,Beijing 100871,China [4]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第5期765-780,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12225102,12050002,12288101,12301555);the National Key R&D Program of China(No.2021YFF1200500);the Taishan Scholars Program of Shandong Province。

摘　　要：The authors 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.They address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.

关 键 词：Saddle point Constrained saddle dynamics Solution landscape Semiimplicit Numerical analysis 

分 类 号：O241.8[理学—计算数学]