Global existence of real roots and random Newton flow algorithm for nonlinear system of equations |
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Authors: | ChuanMiao Chen HongLing Hu |
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Institution: | 1.Key Laboratory of HPCSIP (Ministry of Education of China), College of Mathematics and Computer Science,Hunan Normal University,Changsha,China |
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Abstract: | 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. |
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