Convexity in Newton's 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.

List of contents

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.

Summary

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.

Product details

• Authors: José Antonio Ezquerro Fernandez, José Antonio Ezquerro Fernández, Hernández Verón, Miguel Ángel Hernández Verón
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 06.05.2025
• EAN: 9783031857539
• ISBN: 978-3-0-3185753-9
• No. of pages: 242
• Dimensions: 168 mm x 14 mm x 240 mm
• Weight: 436 g
• Illustrations: XII, 242 p. 48 illus., 35 illus. in color.
• Series: Frontiers in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Functional Analysis, Integral Equations, Operator Theory, banach spaces, boundary value problems, Scalar Equations, Newton-Raphson method, Newton method, Convex functions, Logarithmic convexity, Chebyshev method, Convergence analysis, Kantorovich’s theory, Accelerations of Newton’s method, High-order convergence