Let T: D⊂ X→ X be an iteration function in a complete metric space X. In this paper we
present some new general complete convergence theorems for the Picard iteration xn+ 1 …

This book introduces advanced numerical-functional analysis to beginning computer
science researchers. The reader is assumed to have had basic courses in numerical …

The classical Kantorovich theorem on Newton's method assumes that the derivative of the
operator involved satisfies a Lipschitz condition‖ F′(x)− F′(y)‖≤ L‖ x− y‖. In this …

We present an efficient genetic algorithm as a general tool for solving optimum problems. As
a specialized application this algorithm can be used to approximate a solution of a system of …

In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a
system of nonlinear equations is studied. Two convergence theorems are presented. The …

Inexact Newton methods axe constructed by combining Newton's method with another
iterative method that is used to solve the Newton equations inexactly. In this paper, we …

One kind of the L-average Lipschitz condition is introduced to covariant derivatives of
sections on Riemannian manifolds. A convergence criterion of Newton's method and the …

The present paper is concerned with the convergence problem of Newton's method to solve
singular systems of equations with constant rank derivatives. Under the hypothesis that the …

The famous Newton–Kantorovich hypothesis (Kantorovich and Akilov, 1982 [3], Argyros,
2007 [2], Argyros and Hilout, 2009 [7]) has been used for a long time as a sufficient condition …

In this study, we present a convergence analysis of a Newton-like midpoint method for
solving nonlinear equations in a Banach space setting. The semilocal convergence is …