In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...

Carpathian Journal of Mathematics, Vol. 31, No. 1 (2015), pp. 11-30 (20 pages) We use the method of recurrent functions to provide a new semilocal convergence analysis for secant-like methods in order ...

Abstract: We show that Newton methods for generalized equations are input-to-state stable with respect to perturbations such as due to inexact computations. We then use this result to obtain ...

If the SINGLE option is not used, PROC MODEL computes values that simultaneously satisfy the model equations for the variables named in the SOLVE statement. PROC MODEL provides three iterative methods ...

Abstract: In this paper, a revision of the Newton iteration format for nonlinear equation is proposed on the basis of the existing Newton iterative format. The convergence behavior of the algorithm is ...