Newton’s Method: an Updated Approach of Kantorovich’s Theory - Brossura

Ezquerro Fernández, José Antonio Ezquerro

Brossura

ISBN 10: 3319559753 ISBN 13: 9783319559759

Casa editrice: Birkhäuser, 2017

Riassunto

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.

Su questo libro

Informazioni sull?autore

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. 

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3319559753
• ISBN 13: 9783319559759
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 180
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania