Global existence of real roots and random Newton flow algorithm for nonlinear system of equations

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（7）
• 页码范围: 1341-1352
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11425-015-0492-2

摘要

To solve nonlinear system of equation,F(x) =0,a continuous Newton flow xt(t) =V(x) =-(DF(x))-1F(x),x(0) =x0 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 xj+1 =xj + hV(xj) with random initial value x0 and h ∈ (0,1],and three computable quantities,gj,dj and Kj.The numerical experiments with dimension n =300 are provided.