Hidden Bibliographic Details
| Other authors / contributors: | Verón, Miguel Ángel Hernández, author.
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| ISBN: | 9783319559766
3319559761
9783319559759
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| Notes: | Includes bibliographical references.
Online resource; title from PDF title page (EBSCO, viewed July 13, 2017).
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| Summary: | This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.--
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| Other form: | Print version: Fernández, José Antonio Ezquerro. Newton's method : an updated approach of Kantorovich's theory. Cham, Switzerland : Birkhauser, ©2017 xii, 166 pages Frontiers in mathematics. 1660-8054 9783319559759
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