The Secant/Finite Difference Alogorithm for Solving Sparse Nonlinear Systems of Equations

This paper presents an algorithm, the secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is a combination of a finite difference method and a secant method. A q-superlinear convergence result and an r-convergence rate estimate show that this algorithm has good local convergence properties. The numerical results indicate that this algorithm is probably more efficient than some currently used algorithms