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Numerical Computing with IEEE Floating Point Arithmetic.pdf

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    Numerical Computing with IEEE Floating Point Arithmetic
    ISBN 0-89871-571-7
    Contents
    Preface
    Chapter 1 Introduction
    Chapter 2 The Real Numbers
    Chapter 3 Computer Representation of Numbers
    Chapter 4 IEEE Floating Point Representation
    Chapter 5 Rounding
    Chapter 6 Correctly Rounded Floating Point Operations
    Chapter 7 Exceptions
    Chapter 8 The Intel Microprocessors
    Chapter 9 Programming Languages
    Chapter 10 Floating Point in C
    Chapter 11 Cancellation
    Chapter 12 Conditioning of Problems
    Chapter 13 Stability of Algorithms
    Chapter 14 Conclusion
    Bibliography
    Index
    Numerical Computing with IEEE Floating Point Arithmetic
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    Numerical Computing with IEEE Floating Point Arithmetic Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises Michael L. Overton Courant Institute of Mathematical Sciences New York University New York, New York siam. Society for Industrial and Applied Mathematics Philadelphia
    Copyright © 2001 by the Society for Industrial and Applied Mathematics. 1 0 9 8 7 6 5 4 32 All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688. Library of Congress Cataloging-in-Publication Data Overton, Michael L Numerical computing with IEEE floating point arithmetic / Michael L Overton. p. cm. Includes bibliographical references and index. ISBN 0-89871-571-7 I. Computer arithmetic. 2. Floating-point arithmetic. 3. Numerical calculations. I. Title. QA76.9.M35O94200I O04'.0l'5l--dc2l 00-067941 SlcLJTL is a registered trademark.
    Dedicated to girls who like math especially my daughter Eleuthera Overton Sa
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    Contents Preface Acknowledgments 1 Introduction 2 The Real Numbers 3 Computer Representation of Numbers 4 IEEE Floating Point Representation 5 Rounding 6 Correctly Rounded Floating Point Operations 7 Exceptions 8 The Intel Microprocessors 9 Programming Languages 10 Floating Point in C 11 Cancellation 12 Conditioning of Problems 13 Stability of Algorithms 14 Conclusion Bibliography ix xi 1 5 9 17 25 31 41 49 55 59 71 77 83 97 101 vii
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