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Convexity in Newton's method

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convexity in Newton's methodby José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
作者:	Ezquerro Fernández, José Antonio.
其他作者:	Hernández Verón, Miguel Ángel.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xii, 242 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Convex domains.
電子資源:	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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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.
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