Advances in Iterative Methods for Nonlinear Equations
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applica
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Advances in Iterative Methods for Nonlinear Equations
Se MA
SEMA SIMAI Springer Series Series Editors: Luca Formaggia (Editors-in-Chief) • Pablo Pedregal (Editors-in-Chief) Jean-Frédéric Gerbeau • Tere Martinez-Seara Alonso • Carlos Parés • Lorenzo Pareschi • Andrea Tosin • Elena Vazquez • Jorge P. Zubelli • Paolo Zunino Volume 10
More information about this series at http://www.springer.com/series/10532
Sergio Amat • Sonia Busquier Editors
Advances in Iterative Methods for Nonlinear Equations
123
Editors Sergio Amat Departamento de Matemática Aplicada y Estadística Universidad Politécnica de Cartagena Cartagena, Spain
ISSN 2199-3041 SEMA SIMAI Springer Series ISBN 978-3-319-39227-1 DOI 10.1007/978-3-319-39228-8
Sonia Busquier Departamento de Matemática Aplicada y Estadística Universidad Politécnica de Cartagena Cartagena, Spain
ISSN 2199-305X (electronic) ISBN 978-3-319-39228-8 (eBook)
Library of Congress Control Number: 2016950010 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Contents
1
Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Sergio Amat
1
2
An Overview on Steffensen-Type Methods . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . S. Amat, S. Busquier, Á.A. Magreñán, and L. Orcos
5
3
Newton’s Method for Convex Optimization . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Ioannis K. Argyros and Daniel González
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4
Inexact Newton Methods on Riemannian Manifolds . . . . . . . . . . . . . . . . . . . I.K. Argyros and Á.A. Magreñán
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5
On the Design of Optimal Iterative Methods for Solving Nonlinear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Alicia Cor
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