Generalized Locally Toeplitz Sequences: Theory and Applications Volu
Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related a
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neralized Locally Toeplitz Sequences: Theory and Applications Volume I
Generalized Locally Toeplitz Sequences: Theory and Applications
Carlo Garoni Stefano Serra-Capizzano •
Generalized Locally Toeplitz Sequences: Theory and Applications Volume I
123
Stefano Serra-Capizzano Department of Science and High Technology University of Insubria Como Italy
Carlo Garoni Department of Science and High Technology University of Insubria Como Italy
ISBN 978-3-319-53678-1 DOI 10.1007/978-3-319-53679-8
ISBN 978-3-319-53679-8
(eBook)
The present book has been realized with the financial support of the Italian INdAM (Istituto Nazionale di Alta Matematica) and the European “Marie-Curie Actions” Programme through the Grant PCOFUND-GA-2012-600198. Library of Congress Control Number: 2017932016 © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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
Preface
Sequences of matrices with increasing size naturally arise in several contexts and especially in the discretization of continuous problems, such as integral and differential equations. The theory of generalized locally Toeplitz (GLT) sequences was developed in order to compute/analyze the asymptotic spectral distribution of these sequences of matrices, which in many cases turn out to be GLT sequences. In this book we present the theory of GLT sequences together with some of its main applications. We will also refer the reader to the available literature for further applications that are not included herein. It normally happens in mathematics that ideas are better conveyed in the univariate setting and then transferred to the multivariate setting by successive general
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