|
Showing 1 - 4 of
4 matches in All Departments
Many problems in science and engineering have their mathematical
formulation as an operator equation of the form F(x) = y, where F
is a linear or nonlinear operator between certain function spaces.
In practice, such equations are solved approximately using
numerical methods, as their exact solution may not be often
possible or may not be worth looking for due to physical
constraints. In such situation, it is desirable to know how the
so-called approximate solution approximates the exact solution, and
what would be the error involved in such procedures. The main focus
of the book is on the study of stably solving nonlinear ill posed
operator equations of the form F(x)=y, with monotone nonlinear
operator F in an infinite dimensional real Hilbert space X, that
is, F obeys the monotonicity property. It is assumed that the exact
data y is unknown and usually only noisy data are available.
Problems of this type arise in a number of applications. Since the
solution does not depend continuously on the data, the ill-posed
problem has to be regularized. We considered iterative methods
which converge to the unique solution of the method of Lavrentiev
regularization.
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.
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.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Tenet
John David Washington, Robert Pattinson, …
DVD
R53
Discovery Miles 530
|