Applications of the Differential Calculus
In this chapter our attention is focused on applications of the differential calculus. The first main goal is the numerical solution of nonlinear systems of equations. In particular, Newton-like methods are studied in detail. As a special case the numeric
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hematical Analysis and the Mathematics of Computation
Mathematical Analysis and the Mathematics of Computation
Werner Römisch Thomas Zeugmann •
Mathematical Analysis and the Mathematics of Computation
123
Thomas Zeugmann Division of Computer Science Hokkaido University Sapporo Japan
Werner Römisch Institut für Mathematik Humboldt-Universität zu Berlin Berlin Germany
ISBN 978-3-319-42753-9 DOI 10.1007/978-3-319-42755-3
ISBN 978-3-319-42755-3
(eBook)
Library of Congress Control Number: 2016952899 © 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 The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To our wives, Ute and Yasuyo
Preface
This book aims to provide a comprehensive introduction to the field of (classical) mathematical analysis and mathematics of computation. While many students may have a perception of what mathematical analysis might be, which is often formed in school and college, there is, in our experience, a rather large surprise when studying mathematical analysis at the university level. Concerning mathematics of computation the situation may be even worse. This field is rich and has seen an enormous development during recent decades. It comprises numerical analysis, computational discrete mathematics, including algebra and combinatorics, number theory, and stochastic numerical methods as well as certain aspects related to mathematical optimization. In addition there are many interdisciplinary applications of all these research subjects, e.g., support vector machines, kernel-based learning methods, pattern recognition, statistical learning theory, computer graphics, approximation theory, and many more. So having a solid understanding of the foundations of mathematical analysis and of its relations to the mathematics of computation i
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