This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

Newton's method is often used for solving nonlinear equations. In this paper, we show that
Newton's method converges under weaker convergence criteria than those given in earlier …

A plethora of sufficient convergence criteria has been provided for single-step iterative
methods to solve Banach space valued operator equations. However, an interesting …

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

In this paper we study local convergence of inexact Newton methods of the form
\big(f(x_k)+A_k(x_k+1-x_k)+F(x_k+1)\big)∩R_k(x_k)≠∅\with\A_k∈\calH(x_k) for solving …

The high speed of x_k→x^∗∈\mathbbR is usually measured using the C-, Q-, or R-orders:
\lim|x^∗-x_k+1||x^∗-x_k|^p_0∈(0,+∞),\qquad\lim\ln|x^∗-x_k+1|\ln|x^∗-x_k|=q_0,\qquador …

Twenty years after the classical book of Ortega and Rheinboldt was published, five
definitions for the Q-convergence orders of sequences were independently and rigorously …

We present a local as well as a semi-local convergence analysis of Newton's method for
solving nonlinear equations in a Banach space setting. The new approach leads in the local …

Iterative algorithms requiring the computationally expensive in general inversion of linear
operators are difficult to implement. This is the reason why hybrid Newton-like algorithms …

The implementation of Newton's method for solving nonlinear equations in abstract domains
requires the inversion of a linear operator at each step. Such an inversion may be …