an introduction to numerical analysis for electrical and computer engineers - wiley

TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J. Zarowski University of Alberta, Canada A JOHN WILEY & SONS, INC. PUBLICATION TLFeBOOK TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS TLFeBOOK TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J. Zarowski University of Alberta, Canada A JOHN WILEY & SONS, INC. PUBLICATION TLFeBOOK Copyright c  2004 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Zarowski, Christopher J. An introduction to numerical analysis for electrical and computer engineers / Christopher J. Zarowski. p. cm. Includes bibliographical references and index. ISBN 0-471-46737-5 (coth) 1. Electric engineering—Mathematics. 2. Computer science—Mathematics. 3. Numerical analysis I. Title. TK153.Z37 2004 621.3 ′ 01 ′ 518—dc22 2003063761 Printed in the United States of America. 10987654321 TLFeBOOK In memory of my mother Lilian and of my father Walter TLFeBOOK TLFeBOOK CONTENTS Preface xiii 1 Functional Analysis Ideas 1 1.1 Introduction 1 1.2 Some Sets 2 1.3 Some Special Mappings: Metrics, Norms, and Inner Products 4 1.3.1 Metrics and Metric Spaces 6 1.3.2 Norms and Normed Spaces 8 1.3.3 Inner Products and Inner Product Spaces 14 1.4 The Discrete Fourier Series (DFS) 25 Appendix 1.A Complex Arithmetic 28 Appendix 1.B Elementary Logic 31 References 32 Problems 33 2 Number Representations 38 2.1 Introduction 38 2.2 Fixed-Point Representations 38 2.3 Floating-Point Representations 42 2.4 Rounding Effects in Dot Product Computation 48 2.5 Machine Epsilon 53 Appendix 2.A Review of Binary Number Codes 54 References 59 Problems 59 3 Sequences and Series 63 3.1 Introduction 63 3.2 Cauchy Sequences and Complete Spaces 63 3.3 Pointwise Convergence and Uniform Convergence 70 3.4 Fourier Series 73 3.5 Taylor Series 78 vii TLFeBOOK [...]... Other than accuracy and computer resource issues, ease of implementation is also relevant This is a human labor issue Some methods may be easier to implement on a given set of computing resources than others This would have an impact An Introduction to Numerical Analysis for Electrical and Computer Engineers, by C.J Zarowski ISBN 0-4 7 1-4 673 7-5 c 2004 John Wiley & Sons, Inc 1 TLFeBOOK 2 FUNCTIONAL ANALYSIS. .. than Boolean algebra, convolution integrals, and Fourier or Laplace transforms, all of which are standard fare in present-day electrical and computer engineering curricula Engineering past Engineering present Engineering future Christopher Zarowski TLFeBOOK 1 Functional Analysis Ideas 1.1 INTRODUCTION Many engineering analysis and design problems are far too complex to be solved without the aid of computers... added impetus to the subject, and so it now plays a central role in a large part of engineering analysis, simulation, and design This is so true that no engineer can be deemed competent without some knowledge and understanding of the subject Because of the background of the author, this book tends to emphasize issues of particular interest to electrical and computer engineers, but the subject (and the present... far too closely to particular software tools and/ or programming languages But the highly transient nature of software tools and programming languages often blinds the user to the timeless nature of the underlying principles of analysis Furthermore, it is an erroneous belief that one can successfully employ numerical methods solely through the use of “canned” software without any knowledge or understanding... [1 1]T , and y = √ [1 − 1]T These too form 2 2 an orthogonal basis for the space R2 Define the functions φ(x) = and ψ(x) =      0, x < 0 and x ≥ 1 1, 0 ≤ x < 1 0, x < 0 and x ≥ 1 1, 0 ≤ x < −1, 1 2 1 2 (1.40) (1.41) ≤x . PUBLICATION TLFeBOOK TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS TLFeBOOK TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J electronic format. Library of Congress Cataloging-in-Publication Data: Zarowski, Christopher J. An introduction to numerical analysis for electrical and computer engineers / Christopher J. Zarowski. p TLFeBOOK AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS Christopher J. Zarowski University of Alberta, Canada A JOHN WILEY & SONS, INC. PUBLICATION TLFeBOOK TLFeBOOK AN