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Insight Through Computing Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
Insight Through Computing A MATLAB Introduction to Computational Science and Engineering Charles F. Van Loan K.-Y. Daisy Fan Cornell University Ithaca, New York Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php Society for Industrial and Applied Mathematics
Copyright © 2010 by the Society for Industrial and Applied Mathematics 10 9 8 7 6 5 4 3 2 1 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 Market Street, 6th Floor, Philadelphia, PA 19104-2688 USA. Trademarked names may be used in this book without the inclusion of a trademark symbol. These names are used in an editorial context only; no infringement of trademark is intended. Java is a trademark of Sun Microsystems, Inc. in the United States and other countries. MATLAB is a registered trademark of The MathWorks, Inc. For MATLAB product information, please contact The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA, 508-647-7000, Fax: 508-647-7001, info@mathworks.com, www.mathworks.com. Big Ben image used courtesy of Wikimedia Commons. Cover image and Figure 12.13 used with permission of Cornell University Photography. Library of Congress Cataloging-in-Publication Data Van Loan, Charles F. Insight through computing : a MATLAB introduction to computational science and engineering / Charles F. Van Loan, K.-Y. Daisy Fan. p. cm. Includes index. ISBN 978-0-898716-91-7 1. Numerical analysis--Data processing. 2. Science--Computer simulation. 3. Engineering mathematics--Data processing. 4. MATLAB. I. Fan, K.-Y. Daisy. II. Title. QA297.V25 2010 005.1--dc22 2009030277 is a registered trademark. Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
To our families  Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
Contents xi Preface Programming Topics Software xvii xv 1 27 45 63 1 1.1 From Formula to Program Just Plug It In! 3 Surface Area of a Sphere Matlab: Arithmetic expressions, assignment, input, output 1.2 Check and Evaluate 14 Minimum of a Quadratic on an Interval Matlab: Boolean expressions, conditionals 2 2.1 Limits and Error Tiling a Disk Summation Matlab: The for-loop 29 2.2 Inside/Outside Polygons 36 Sequences Matlab: The while-loop 3 3.1 Approximation with Fractions 22/7ths and Counting 47 Proximity to Pi Matlab: Nested loops, benchmarking 3.2 Not Quite Perfect 56 Fibonacci Quotients and the Golden Ratio Matlab: More complicated while-loops 4 4.1 4.2 The Discrete versus the Continuous Connect the Dots 65 Plotting Continuous Functions Matlab: Vectors, elementary graphics From Cyan to Magenta Color Computations Matlab: rgb 79 4.3 One Third Plus One Third Is Not Two Thirds 87 The Floating Point Environment Matlab: eps, inf, NaN vii Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
viii 5 5.1 Abstraction Reshaping Rectangles A Square and a Root Matlab: Simple functions 97 5.2 Oval Odometer 109 Ellipse Perimeter Matlab: Functions with multiple input parameters 5.3 The Betsy Ross Problem 118 Design Parameters Matlab: Graphics functions 6 6.1 6.2 Randomness Safety in Numbers 131 Monte Carlo Simulation Matlab: More practice with boolean expressions Dice and Compass Random Walks Matlab: More practice with while-loops 143 6.3 Order from Chaos 149 Polygon Averaging Matlab: More practice with graphics and vectors 7 The Second Dimension 7.1 From Here to There 157 Transition Matrices Matlab: Two-dimensional arrays 7.2 Contours and Cross Sections 166 Visualizing F (x, y) Matlab: Contour plotting 7.3 Cool It! 171 Simulation on a Grid Matlab: A(i,j) updating 8 Reordering 8.1 Cut and Deal 181 The Perfect Shuffle Matlab: More practice with vectors and subscripting 8.2 188 Size Place Sorting Matlab: sort Contents 95 129 155 179 Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
Contents 9 9.1 9.2 9.3 Search Patterns in Proteins 199 Linear Search Matlab: Character arrays A Roman Numeral Phone Book Binary Search Matlab: Cell arrays 219 Changing Sign Bisecting for Roots Matlab: Functions as parameters 208 Points, Polygons, and Circles 10 10.1 How Far? 229 Distance Metrics Matlab: Simple structures 10.2 Fenced in Twice? 237 Intersection Matlab: More complicated structures, boolean-valued functions 10.3 Not Perfect? 244 Nearness in Shape Matlab: Practice with structures 11 Text File Processing 11.1 Latitude and Daylight 257 Data Acquisition and Conversion Matlab: Reading data from a text file 11.2 Nearby Millions 268 Writing and Representation Matlab: Creating .dat and .bin files The Matrix: Part II 12 12.1 Saving Private Rainbows 285 Linear Interpolation and Color Mapping Matlab: row-by-row matrix setup 12.2 Known on the Corner 292 Bilinear Interpolation and Shading Matlab: from f (x, y) toF(i,j) 12.3 Seven-by-Five 299 ix 197 227 255 283 Image Digitization Matlab: Cell arrays of matrices 12.4 Picture This 306 Working with Image Data Files Matlab: imread, imwrite, more practice with matrices Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
x 13 Acoustic File Processing 321 13.1 The Clock Strikes Acquisition and Playback Matlab: wavread, sound, wavwrite 13.2 Dial N for Noise 326 Frequency and Sampling Matlab: More practice with vectors 14 Divide and Conquer 14.1 Patterns within Patterns 337 Recursive Tiling Matlab: Recursive functions 14.2 N and Half N Merge Sort Matlab: More practice with recursion 344 14.3 Looking for Trouble 354 Adaptive Interpolation Matlab: Still more practice with recursion 15 Optimization 15.1 Shortest Route 365 The Combinatoric Explosion Matlab: More practice with arrays 15.2 Best Bike 372 Constraints and Objective Functions Matlab: More complicated nested loops 15.3 Most Likely Orbit Model Building Matlab: Interactive search 381 Appendix A. Refined Graphics Appendix B. Mathematical Facts Appendix C. MATLAB, Java, and C Appendix D. Exit Interview Index Contents 319 335 363 389 411 417 423 425 Downloaded 13 May 2012 to 202.201.0.66. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php
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