包含coursera上Nathan Kutz（本书作者）两门课的内容，设计数值分析，信号与图像处理，数学建模等。
This page intentionally left blank Data-Driven Modeling Scientific Computation Methods for Complex Systems 8 Big Data ). NATHAN KUTZ Department of applied Mathematics University of Washington OⅩFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford, OX2 6DP United Kingdom Oxford University Press is a department of the university of oxford It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide Oxford is a registered trade mark of xford University Press in the UK and in certain other countries CJ. Nathan Kutz 2013 The moral rights of the author have been asserted First Edition published in 2013 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the united States of america by oxford University Press 198 Madison avenue. New york, ny 10016, United States of america British library catalo Data Data available Library of Congress Control Number: 2013937977 ISBN978-0-19-966033-9(hbk ISBN978-0-19-966034-6(pbk) Printed and bound by CPI Group(UK)Ltd, Croydon, CRO 4YY party e p d faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work Dedication For Kristy, Lauren and Katie Acknowledgments The idea of the first part of this book began as a series of conversations with Dave muraki It then grew into the primary set of notes for a scientific computing course whose ambition was to provide a truly versatile and useful course for students in the engineering, biological and phys ical sciences. And over the last couple of years, the book expanded to included methods for data analysis, thus bolstering the intellectual scope of the book significantly Unbeknownst to them much of the data analysis portion of the book was heavily inspired by the fantastic works of Emmanuel candes, yannis Kevrekidis and clancy rowley and various conversations i had with each of them. I ve also benefitted greatly from early discussions with James Rossmanith, and with implementation ideas with Peter Blossey and Sorin Mitran; and more recently on dimension ality reduction methods with Steven Brunton, Edwin Ding, Joshua Proctor, Peter Schmid,Eli Shlizerman, Jonathan Tu and matthew williams. Leslie Butson, Sarah hewitt and Jennifer o neil have been very helpful in editing the book so that it is more readable, useful and error-free. a special thanks should also be given to all the many wonderful students who have provided so much critical commentary and vital feedback for improving the delivery, style and correctness of the book. Of course, all errors in this book are the fault of my daughters hamsters Fluffy and Quickies Contents Prolegomenon How to Use this book About MatLaB PART I Basic Computations and visualization MATLAB Introduction 1.1 Vectors and matrices 339 1.2 Logic, Loops and Iterations 1.3 Iteration: The Newton-Raphson Method 13 1.4 Function Calls, Input/Output Interactions and Debugging 18 1.5 Plotting and Importing/Exporting Data 23 2Linear Systems 2.1 Direct solution methods for ax= b 31 2.2 Iterative Solution Methods for ax= b 35 2.3 Gradient(Steepest)Descent for Ax=b 39 2.4 Eigenvalues, Eigenvectors and Solvability 2.5 Eigenvalues and Eigenvectors for Face Recognition 49 2.6 Nonlinear Systems 56 3Curve Fitting 61 3.1 Least-Square Fitting Methods 61 3.2 Polynomial Fits and Splines 65 3.3 Data Fitting with MATLAB 69 4Numerical Differentiation and Integration 77 4.1 Numerical differentiation 4.2 Numerical Integration 8 4.3 Implementation of Differentiation and Integration 87 vIll CONTENTS 5 Basic Optimization 93 Unconstrained Optimization(Derivative-Free Methods) 93 5.2 Unconstrained Optimization(Derivative Methods) 99 5.3 Linear Programming 105 5.4 Simplex Method 110 5.5 Genetic Algorithms 113 vIsualization 119 6.1 Customizing Plots and Basic 2D Plotting 119 6.2 More 2D and 3D Plotting 125 6.3 Movies and animations 131 PART II Differential and Partial Differential Equations Initial and Boundary Value Problems of Differential Equations 137 7.1 Initial Value Problems: Euler, Runge-Kutta and Adams methods 137 7.2 Error Analysis for Time-Stepping Routines 144 7.3 Advanced Time-Stepping Algorithms 149 7.4 Boundary Value Problems: The Shooting Method 153 7.5 Implementation of Shooting and Convergence studies 160 7.6 Boundary Value Problems: Direct Solve and Relaxation 164 7.7 Implementing MATLAB for Boundary Value Problems 167 7.8 Linear Operators and Computing Spectra 8Finite Difference Methods 80 8.1 Finite Difference discretization 180 8.2 Advanced Iterative Solution methods for ax= b 186 8.3 Fast Poisson Solvers: The fourier transform 186 8.4 Comparison of Solution Techniques for Ax= b: Rules of Thumb 190 8.5 Overcoming Computational Difficulties 195 9Time and Space Stepping Schemes: Method of Lines 200 9.1 Basic Time-Stepping Schemes 200 9.2 Time-Stepping Schemes: Explicit and Implicit Methods 205 9.3 Stability Analysis 209 CONTENTS 9.4 Comparison of Time-Stepping Schemes 213 9.5 Operator Splitting Techniques 216 9.6 Optimizing Computational Performance: Rules of Thumb 219 10 Spectral Methods 225 10.1 Fast Fourier Transforms and Cosine/Sine Transform 225 10.2 Chebychev polynomials and Transform 229 10.3 Spectral Method Implementation 233 10.4 Pseudo-Spectral Techniques with Filtering 235 0.5 Boundary Conditions and the Chebychev Transform 240 10.6 Implementing the Chebychev Transform 244 10.7 Computing Spectra: The Floquet-Fourier-Hill Method 249 11 Finite Element Methods 256 11.1 Finite element basis 256 11.2 Discretizing with Finite Elements and Boundaries 261 11.3 MATLAB for Partial Differential Equations 266 11.4 MATLAB Partial Differential Equations Toolbox 271 PART Ill Computational Methods for data analysis 12 Statistical Methods and Their Applications 279 12.1 Basic Probability Concepts 279 12.2 Random Variables and Statistical Concepts 286 12.3 Hypothesis Testing and Statistical Significance 294 3Time-Frequency Analysis: Fourier Transforms and Wavelets 301 13.1 Basics of fourier series and the fourier transform 301 13.2 FFT Application: Radar Detection and Filtering 308 13.3 FFT Application: Radar Detection and Averaging 316 13.4 Time-Frequency Analysis: Windowed Fourier Transforms 322 13.5 Time-Frequency Analysis and Wavelets 328 13.6 Multi-Resolution Analysis and the wavelet basis 335 13.7 Spectrograms and the Gabor Transform in MATLAB 340 3.8 MATLAB Filter Design and Wavelet Toolboxes 346