Numerical Eigenvalue Problems
No, we have seen that 4n3/3 operations are required in order to bring a matrix to upper triangular form using Householder transformations.
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Tom Lyche · Georg Muntingh Øyvind Ryan
Exercises in Numerical Linear Algebra and Matrix Factorizations
Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick
Texts in Computational Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick
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More information about this series at http://www.springer.com/series/5151
Tom Lyche • Georg Muntingh • Øyvind Ryan
Exercises in Numerical Linear Algebra and Matrix Factorizations
Tom Lyche Blindern University of Oslo Oslo, Norway
Georg Muntingh SINTEF ICT Oslo, Norway
Øyvind Ryan Blindern University of Oslo Oslo, Norway
ISSN 1611-0994 ISSN 2197-179X (electronic) Texts in Computational Science and Engineering ISBN 978-3-030-59788-7 ISBN 978-3-030-59789-4 (eBook) https://doi.org/10.1007/978-3-030-59789-4 Mathematics Subject Classification (2010): 15-XX, 65-XX © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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, expressed 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. Cover illustration: A steepest descent iteration (left) and a conjugate gradient iteration (right) to find the minimum of a quadratic surface shown by some level curves. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To our families:
Annett, Max, Ella, and Mina;
Natalia, Katrina, and Alina.
Preface
The starting point for these solutions is a course in numerical linear algebra at the University of Oslo. Tom Lyche wrote and gradually expanded a text for this course over a period of more than 30 years. He also expanded the text with many new exercises, and many exam questions were made over the years as well. This work ultimately ended in the book “Numerical Li
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