Convexity in Newton's Method
Description
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.
Reviews / Votes
"The three volumes can be read independent from each other. The text is clearly written by reducing much of the analysis to the scalar case and giving many examples that illustrate the concepts." (Adhemar Bultheel, zbMATH 1573.65004, 2026)
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Content
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.
