The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear
least squares problems. It is particularly well suited to the treatment of very large scale …

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

A classical model of Newton iterations which takes into account some error terms is given by
the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high …

Motivated by machine learning problems over large data sets and distributed optimization
over networks, we develop and analyze a new method called incremental Newton method …

The problem of four‐dimensional variational data assimilation can be considered as a non‐
linear least squares problem. A common method for solving it is equivalent to a Gauss …

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 …

Often in nature different systems interact, like fluids and structures, heat and electricity,
populations of species, etc. It is our aim in this thesis to find, describe and analyze solution …

The dogleg method is a classical trust-region technique for globalizing Newton's method.
While it is widely used in optimization, including large-scale optimization via truncated …

A Newton–Krylov method is an implementation of Newton's method in which a Krylov
subspace method is used to solve approximately the linear systems that characterize steps …