On the Second Order Convergence of Brown's Derivative-Free Method for Solving Simultaneous Nonlinear Equations.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1971
- Accession Number
- AD0732796
Entities
People
- J. E. Dennis Jr.
- Kenneth M. Brown
Organizations
- Yale University