Newton's method : an updated approach of Kantorovich's theory / José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
Fernández, José Antonio Ezquerro, author.; Verón, Miguel Ángel Hernández, author.
2017
QA297.8
Available Online

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Title Newton's method : an updated approach of Kantorovich's theory / José Antonio Ezquerro Fernández, Miguel Ángel Hernández Verón.
Author Fernández, José Antonio Ezquerro, author.
ISBN 9783319559766 (electronic book)
3319559761 (electronic book)
9783319559759
Published Cham, Switzerland : Birkhäuser, 2017.
Language English
Description 1 online resource.
Call Number QA297.8
Dewey Decimal Classification 518.26
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.-- Provided by publisher.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (viewed July 13, 2017).
Added Author Verón, Miguel Ángel Hernández, author.
Series Frontiers in mathematics. 1660-8054
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Record Appears in Online Resources > Ebooks
All Resources
The classic theory of Kantorovich
Convergence conditions on the second derivative of the operator
Convergence conditions on the k-th derivative of the operator
Convergence conditions on the first derivative of the operator.

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