Global Damping Algorithm For Nonlinear Equations

In nonlinear science and technology,it is very important to solve nonlinear equations.On the basis of Newton method,the paper introduces Random New-ton Flow Algorithm and Global Damping Algorithm for Nonlinear Equations.At first,we analyze the Newtonian flow V(x)=-(DF(xk))-1F(xk) of the three structural features:1.the central field structure.2.The nature of the root existence.3.the structure of the odd surface.Random Newton Flow Algorithm is based on this structure,for solving large-scale nonlinear equations.And for solving the problem of odd surface in Random Newton Flow Algorithm,we put forward the Global Damping flow W(x) instead the Newton Flow V(a:),thereby, bring about a wide range of convergence.The Random Newton Flow Algorithm and Global Damping Algorithm are the Quadratic Convergence.The Random Newton Flow Algorithm is able to identify singularities and root convergence to the root. And the Global Damping Algorithm can root convergence to the root from random initial point without the odd surface. Main characteristics of the both algorithm is the ability to randomly cast point search either convergence to the root singularity.In the last,we constructs a high-dimensional equation,taking a large num-ber of random initial points, in the sense of probability 1,RNF can find all isolated roots, including real, complex and multiple roots.