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Newton's method = an updated approach of Kantorovich's theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Newton's method/ by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
Reminder of title:	an updated approach of Kantorovich's theory /
Author:	Ezquerro Fernandez, Jose Antonio.
other author:	Hernandez Veron, Miguel Angel.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xii, 166 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Newton-Raphson method. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-55976-6
ISBN:	9783319559766

Newton's method = an updated approach of Kantorovich's theory /
Ezquerro Fernandez, Jose Antonio.

Newton's methodan updated approach of Kantorovich's theory /[electronic resource] :by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron. - Cham :Springer International Publishing :2017. - xii, 166 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

The classic theory of Kantorovich -- Convergence conditions on the second derivative of the operator -- Convergence conditions on the k-th derivative of the operator -- Convergence conditions on the first derivative of the operator.

This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.

ISBN: 9783319559766

Standard No.: 10.1007/978-3-319-55976-6doiSubjects--Topical Terms:

528526
Newton-Raphson method.

LC Class. No.: QA297.8

Dewey Class. No.: 518.26

Newton's method = an updated approach of Kantorovich's theory /
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490 1 $a Frontiers in mathematics, $x 1660-8046
505 0 $a The classic theory of Kantorovich -- Convergence conditions on the second derivative of the operator -- Convergence conditions on the k-th derivative of the operator -- Convergence conditions on the first derivative of the operator.
520 $a This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.
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