This book is dedicated to the approximation of solutions of
nonlinear equations using iterative methods. The study about
convergence matter of iterative methods is usually based on two
categories: semi-local and local convergence analysis. The
semi-local convergence category is, based on the information around
an initial point, to provide criteria ensuring the convergence of
the method; while the local one is, based on the information around
a solution, to find estimates of the radii of the convergence
balls. The book is divided into two volumes. The chapters in each
volume are self-contained so they can be read independently. Each
chapter contains semi-local and local convergence results for
single, multi-step and multi-point old and new contemporary
iterative methods involving Banach, Hilbert or Euclidean valued
operators. These methods are used to generate a sequence defined on
the aforementioned spaces that converges with a solution of a
nonlinear equation, an inverse problem or an ill-posed problem. It
is worth mentioning that most problems in computational and related
disciplines can be brought in the form of an equation using
mathematical modelling. The solutions of equations can be found in
analytical form only in special cases. Hence, it is very important
to study the convergence of iterative methods. The book is a
valuable tool for researchers, practitioners, graduate students,
and can also be used as a textbook for seminars in all
computational and related disciplines.
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