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Convexity in Newton's method

Record Type:	Electronic resources : Monograph/item
Title/Author:	Convexity in Newton's methodby José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
Author:	Ezquerro Fernández, José Antonio.
other author:	Hernández Verón, Miguel Ángel.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xii, 242 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Convex domains.
Online resource:	https://doi.org/10.1007/978-3-031-85754-6
ISBN:	9783031857546$q(electronic bk.)

Convexity in Newton's method
Ezquerro Fernández, José Antonio.

Convexity in Newton's method[electronic resource] /by José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón. - Cham :Springer Nature Switzerland :2025. - xii, 242 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

The degree of logarithmic convexity -- The Newton method and convexity -- Accelerations of the Newton method -- Newton-like methods with high order of convergence -- Optimization of the Chebyshev method.

This monograph examines a variety of iterative methods in Banach spaces with a focus on those obtained from the Newton method. Together with the authors' previous two volumes on the topic of the Newton method in Banach spaces, this third volume significantly extends Kantorovich's initial theory. It accomplishes this by emphasizing the influence of the convexity of the function involved, showing how improved iterative methods can be obtained that build upon those introduced in the previous two volumes. Each chapter presents theoretical results and illustrates them with applications to nonlinear equations, including scalar equations, integral equations, boundary value problems, and more. Convexity in Newton's Method will appeal to researchers interested in the theory of the Newton method as well as other iterative methods in Banach spaces.

ISBN: 9783031857546$q(electronic bk.)

Standard No.: 10.1007/978-3-031-85754-6doiSubjects--Topical Terms:

198918
Convex domains.

LC Class. No.: QA639.5

Dewey Class. No.: 515.882

Convexity in Newton's method
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245 1 0 $a Convexity in Newton's method $h [electronic resource] / $c by José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
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300 $a xii, 242 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8054
505 0 $a The degree of logarithmic convexity -- The Newton method and convexity -- Accelerations of the Newton method -- Newton-like methods with high order of convergence -- Optimization of the Chebyshev method.
520 $a This monograph examines a variety of iterative methods in Banach spaces with a focus on those obtained from the Newton method. Together with the authors' previous two volumes on the topic of the Newton method in Banach spaces, this third volume significantly extends Kantorovich's initial theory. It accomplishes this by emphasizing the influence of the convexity of the function involved, showing how improved iterative methods can be obtained that build upon those introduced in the previous two volumes. Each chapter presents theoretical results and illustrates them with applications to nonlinear equations, including scalar equations, integral equations, boundary value problems, and more. Convexity in Newton's Method will appeal to researchers interested in the theory of the Newton method as well as other iterative methods in Banach spaces.
650 0 $a Convex domains. $3 198918
650 0 $a Newton-Raphson method. $3 229208
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Operator Theory. $3 274795
700 1 $a Hernández Verón, Miguel Ángel. $3 991562
710 2 $a SpringerLink (Online service) $3 273601
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830 0 $a Frontiers in mathematics. $3 558254
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950 $a Mathematics and Statistics (SpringerNature-11649)