On the Second Order Convergence of Brown's Derivative-Free Method for Solving Simultaneous Nonlinear Equations.

摘要

In the paper the authors consider the system f(1)(x(1), x(2), ... ,x(N)) = 0, f(2)(x(1), x(2), ... , x(N)) = 0, 000, f(N)(x(1), x(2), ... , x(N)) = 0,or in vector notation as F(x) = 0. Here the authors assume that each f(i) is real-valued and continuously differentiable and that the x(i) are real;typically one may have N real,transcendental equations in N real unknowns. The problem of solving such a system of nonlinear equations falls conveniently into three subproblems,namely (a) proceeding from perhaps poor initial estimates in some regular fashion into a region of local convergence; (b) using a rapidly convergent,computationally efficient and stable algorithm local to the root;and (c) obtaining further solutions -different from those previously found -of the system. The authors concentrate their efforts on (b). (Author)