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