Convexity in Newton's Method
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Beschreibung
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.
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.
Examines a variety of iterative methods in Banach spaces with an emphasis on those obtained from the Newton method Extends Kantorovich’s theory for the Newton method by illustrating improved iterative methods developed by the authors Constitutes the third in the authors’ trilogy dedicated to the topic of the Newton method in Banach spaces
Autor*in
José Antonio Ezquerro Fernández
Themen in »Convexity in Newton's Method«
Newton method Newton-Raphson method Banach spaces Kantorovich’s theory Logarithmic convexity Convex functions Scalar equations Accelerations of Newton’s method Chebyshev method High-order convergence Convergence analysis Boundary value problems Integral equations
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“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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