Global existence of real roots and random Newton flow algorithm for nonlinear system of equations To memorize Qin's method for 770 anniversaries

作     者：CHEN ChuanMiao HU HongLing 

作者机构：Key Laboratory of HPCSIP(Ministry of Education of China)College of Mathematics and Computer ScienceHunan Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2017年第60卷第7期

页      面：1341-1352页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China(Grant Nos. 11301176 11071067 and 11226332) 

主　　题：nonlinear system of equation continuous Newton flow real roots global existence and uniqueness random Newton flow algorithm 

摘      要：To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are *** concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_*** numerical experiments with dimension n=300 are provided.