Eigenvalue Problems: Numerical Simulations
In this chapter a numerical scheme is proposed to simulate the evolution of the solution\(\vec{x}(t)\) of dynamical system (4.1) towards an eigenvector of a given matrix, and some examples and applications are presented. The method has a linear convergenc
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Luis V´azquez • Salvador Jim´enez
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
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Luis V´azquez Departamento de Matem´atica Aplicada Facultad de Inform´atica Universidad Complutense de Madrid and Real Academia de Ciencias Exactas, F´ısicas y Naturales Spain
Salvador Jim´enez Departamento de Matem´atica Aplicada a las TT.II. E.T.S.I. Telecomunicaci´on Universidad Polit´ecnica de Madrid Spain
ISBN 978-1-4614-5911-8 ISBN 978-1-4614-5912-5 (eBook) DOI 10.1007/978-1-4614-5912-5 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012951341 © Springer Science+Business Media New York 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Luciana and Jos´e Luis with whom I enjoyed many fierce pinball matches in El Escorial and Forte dei Marmi, Luis V´azquez To my beloved ones, Salvador Jim´enez
Preface
In a Pinball Machine, the player tries to score points by manipulating a metal ball on a playing field inside a glass covered case. The objectives of the game are to score as many points as possible, to earn free games and to maximize the time spent playing by earning extra balls and keeping balls in play as long as possible. Apart from the new c
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