國立高雄大學圖資館 |

Language: English

Back

Mild differentiability conditions fo...

Ezquerro Fernandez, Jose Antonio.

Mild differentiability conditions for Newton's method in Banach spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mild differentiability conditions for Newton's method in Banach spacesby Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
Author:	Ezquerro Fernandez, Jose Antonio.
other author:	Hernandez Veron, Miguel Angel.
Published:	Cham :Springer International Publishing :2020.
Description:	xiii, 178 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Banach spaces.
Online resource:	https://doi.org/10.1007/978-3-030-48702-7
ISBN:	9783030487027$q(electronic bk.)

Mild differentiability conditions for Newton's method in Banach spaces
Ezquerro Fernandez, Jose Antonio.

Mild differentiability conditions for Newton's method in Banach spaces[electronic resource] /by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron. - Cham :Springer International Publishing :2020. - xiii, 178 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

Preface -- The Newton-Kantorovich theorem -- Operators with Lipschitz continuous first derivative -- Operators with Holder continuous first derivative -- Operators with Holder-type continuous first derivative -- Operators with w-Lipschitz continuous first derivative -- Improving the domain of starting points based on center conditions for the first derivative -- Operators with center w-Lipschitz continuous first derivative -- Using center w-Lipschitz conditions for the first derivative at auxiliary points.

In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors' technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich's majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton's method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich's theory for Newton's method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.

ISBN: 9783030487027$q(electronic bk.)

Standard No.: 10.1007/978-3-030-48702-7doiSubjects--Topical Terms:

199048
Banach spaces.

LC Class. No.: QA322.2 / .E978 2020

Dewey Class. No.: 515.732

Mild differentiability conditions for Newton's method in Banach spaces
LDR:02769nmm a2200337 a 4500 001 583755
003 DE-He213
005 20201117095515.0
006 m d
007 cr nn 008maaau
008 210202s2020 sz s 0 eng d
020 $a 9783030487027$q(electronic bk.)
020 $a 9783030487010$q(paper)
024 7 $a 10.1007/978-3-030-48702-7 $2 doi
035 $a 978-3-030-48702-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA322.2 $b .E978 2020
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.732 $2 23
090 $a QA322.2 $b .E99 2020
100 1 $a Ezquerro Fernandez, Jose Antonio. $3 789657
245 1 0 $a Mild differentiability conditions for Newton's method in Banach spaces $h [electronic resource] / $c by Jose Antonio Ezquerro Fernandez, Miguel Angel Hernandez Veron.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a xiii, 178 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8046
505 0 $a Preface -- The Newton-Kantorovich theorem -- Operators with Lipschitz continuous first derivative -- Operators with Holder continuous first derivative -- Operators with Holder-type continuous first derivative -- Operators with w-Lipschitz continuous first derivative -- Improving the domain of starting points based on center conditions for the first derivative -- Operators with center w-Lipschitz continuous first derivative -- Using center w-Lipschitz conditions for the first derivative at auxiliary points.
520 $a In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors' technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich's majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton's method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich's theory for Newton's method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.
650 0 $a Banach spaces. $3 199048
650 0 $a Differential algebra. $3 665348
650 1 4 $a Operator Theory. $3 274795
650 2 4 $a Numerical Analysis. $3 275681
650 2 4 $a Integral Equations. $3 274836
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Partial Differential Equations. $3 274075
700 1 $a Hernandez Veron, Miguel Angel. $3 789658
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Frontiers in mathematics. $3 558254
856 4 0 $u https://doi.org/10.1007/978-3-030-48702-7
950 $a Mathematics and Statistics (SpringerNature-11649)