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Newton’s Method: an Updated Approach of Kantorovich’s Theory by Jose Antonio Ezquerro Fernandez
Newton’s Method: an Updated Approach of Kantorovich’s Theory by Jose Antonio Ezquerro Fernandez
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Newton’s Method: an Updated Approach of Kantorovich’s Theory

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Description

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.

Author Biography:

José Antonio Ezquerro is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain. M. A. Hernández-Verón is Professor at the Department of Mathematics and Computation at the University of La Rioja in Spain. 
Release date Australia
July 14th, 2017
Audience
  • Professional & Vocational
Edition
1st ed. 2017
Illustrations
19 Illustrations, color; XII, 166 p. 19 illus. in color.
Pages
166
ISBN-13
9783319559759
Product ID
26800568

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