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 

机构地区：[1]Key Laboratory of HPCSIP(Ministry of Education of China),College of Mathematics and Computer Science,Hunan Normal University

出　　处：《Science China Mathematics》2017年第7期1341-1352,共12页中国科学：数学（英文版）

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

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 studied.We 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_j.The numerical experiments with dimension n=300 are provided.To solve nonlinear system of equation,F（x） = 0,a continuous Newton flow xt（t） = V（x） =-（DF（x））^-1F（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 studied.We 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,gj,dj and Kj.The numerical experiments with dimension n=300 are provided.

关 键 词：nonlinear system of equation continuous Newton flow real roots global existence and uniqueness random Newton flow algorithm 

分 类 号：O175[理学—数学]