数值分析.pdf

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清晰版数值分析,高清英文原版。清晰版数值分析,高清英文原版。
Preface Algorithms As in previous editions, we give a detailed, structured algorithm without program listing for each method in the text. The algorithms are in a form that can be coded, even by those with limited programming experience This edition includes a disk containing programs for solutions to representative exer- cises using the algorithms. The programs for each algorithm are written in Fortran, Pascal, and c. In addition, we have coded the programs using maple and mathematica, as well as in MAtLAB a computer software package that is widely used for linear algebra applica tions. This should ensure that a set of programs is available for most common computin yster A Student Study Guide is available with this edition that illustrates the calls required for these programs, which is useful for those with limited programming experience. The study guide also contains worked-out solutions to many of the problems Brooks/ Cole can provide instructors with an Instructor's Manual that provides an swers and solutions to all the exercises in the book computation results in the instructor's Manual were regenerated for this edition, using the programs on the disk to ensure com- patibility among the various programming systems The algorithms in the text lead to programs that give correct results for the examples and exercises in the text, but no attempt was made to write general-purpose professional software. Specifically, the algorithms are not always written in a form that leads to the most eficient program in terms of either time or storage requirements. When a confict occurred between writing an extremely efficient algorithm and writing a slightly different one that better illustrates the important features of the method the latter path was invariably taken About the Program Disk The Cd on the inside back cover of the book contains programs for all the algorithms in the book, in numerous formats, as well as samples of the Student Study guide for the book in both the PostScript(PS)and the Adobe Portable Document(PDF)formats For each algoithm there is a C, Fortran, Maple, Mathematica, MATLAB, and Pascal program, and for some of these systems there are multiple programs that depend on the particular version of the software that is being run. Every program is illustrated with a sample problem that is closely correlated to the text. This permits the program to be run initially in the language of your choice to see the fom of the input and output. The pro grams can then be modified for other problems by making minor changes. The form of the input and output are, as nearly as possible, the same in each of the programming systems This permits an instructor using the programs to discuss them generically, without regard to the particular programming system an individual student uses The programs are designed to run on a minimally configured computer. All that is re quired is a computer running Ms-DOs, Windows, or the Macintosh operating system You will, however, need appropriate software, such as a compiler for Pascal, Fortran, and C, or one of the computer algebra systems(Maple, Mathematica, and matlAB).There Preface are six subdirectories on the disk, one for each of the computer languages and the accom panying data iles All of the programs are given as aSCII files or worksheets. They can be altered using any editor or word processor that creates a standard asCII file. (These are also commonly called Text Only" fles.) Extensive README files are included with the program fles so that the peculiarities of the various programming systems can be individually addressed. The README files are presented both in ASCI format and as PDF files. As new software is developed, the lgorithms will be updated and placed on the web site for the book. Suggested Course Outlines Numerical Analysis is designed to allow instructors flexibility in the choice of topics, as well as in the level of theoretical rigor and in the emphasis on applications. In line with these aims, we provide detailed references for the results that are not demonstrated in the text and for the applications that are used to indicate the practical importance of the methods. The text references cited are those most likely to be available in college libraries and have been updated to refect the most recent edition at the time this book was placed into production. We also include quotations from original research papers when we feel this material is accessible to our intended audience The following flowchart indicates chapter prerequisites. The only deviation from this chart is described in the footnote at the bottom of the first page of Section 3. 4. Most of the possible sequences that can be generated from this chart have been taught by the authors at Youngstown State University hapter 1 Chapter 2 Chapter 6 Chapter 3 Chapter 10 Chapter Chapter 8 Chapter 4Chapter5 Chapter 9 apter Chapter 12 Preface xiii Acknowledements We feel most fortunate to have had so many of our students and colleagues communicate with us regarding their impressions of earlier editions of this book. All of these comments are taken very seriously; we have tried to include all the suggestions that are in line with the philosophy of the book, and are extremely grateful to all those that have taken the time to contact us and inform us of improvements we can make in subsequent versions We would particularly like to thank the following, whose efforts we greatly appreciate Glen Granzow, Idaho State University Jose Miguel, Universidad Peruana cayetano Heredia, Lima, Peru John m. neue Northern Arizona University L G. de Pillis, Harvey Mudd college We want especially to thank our friend and former student Jim Baglama of Ball State University. Jim agreed to be an extensive reviewer for this edition and was particularly helpful in updating our survey sections and references to software. It is most gratifying to see one's students move through the profession Also moving through his profession, but in a completly different manner, is our Editor and Publisher Gary Ostedt Gary has been an outstanding manager of our projects and a good personal friend. We will very much miss his direction and assistance, and would like to take this opportunity to wish him all the best in his upcoming retirement from Brooks/cole As has been our practice in past editions of the book, we have used student help at Youngstown State University in preparing the seventh edition. Our able assistant for this edition was laurie marinelli. whom we thank for all her work. We would also like to express gratitude to our colleagues on the faculty and administration of Youngstown State University for providing us the opportunity and facilities to complete this project Finally, we would like to thank all those who have used and adopted the various edi tions of Numerical analysis over the years. It has been wonderful to hear from so many students, and new faculty, who used our book for their first exposure to the study of nu merical methods. We hope this edition continues the trend and adds to the enjoyment of students studying numerical analysis. If you have any suggestions for improvements that can be incorporated into future editions of the book, we would be grateful for your com ments. We can be contacted by electronic mail at the addresses listed below. Richard L burden burden @math. ysu edi J. Douglas faires faires @math. ysu. edu Contents Mathematical preliminaries 1 1 Review of calculus 2 1.2 Roundoff errors and computer arithmetic 18 1.3 Algorithms and Convergence 31 merical software 40 Solutions of equations in One variable 47 2.1 The Bisection Method 48 2.2 Fixed 55 2.3 Newton's Method 66 2.4 Error Analysis for Iterative Methods 78 2.5 Accele ating c ence 86 2.6 Zeros of polynomials and Miller' s Method 91 2.7 Survey of Methods and software 101 Interpolation and polynomial Approximation 104 lation and the lagrange poly 1107 3.2 Divided differences 122 3.3 Hermite Interpolation 133 3.4 Cubic Spline Inter 3.5 Parametric Curves 156 3.6 Survey of Methods and Software 163 Contents Numerical differentiation and Integration 166 4.1 Numerical differentiation 167 4.2 Richardsons Extrapolation 178 4.3 Elements of Numerical Integration 186 4.4 Composite Numerical Integration 196 4.5 Romberg Integration 207 4.6 Adaptive Quadrature Methods 213 4.7 Gaussian Quadrature 220 4.8 Multiple Integrals 227 4.9 Improper Integrals 241 4.10 Survey of Methods and Software 247 Initial-value Problems for Ordinary Differential equations 249 5.1 The Elementary Theory of Initial-Value Problems 251 52 Euler’ s Method256 5.3 Higher-Order Taylor Methods 266 5.4 Runge-Kutta Methods 272 5.5 Error Control and the runge -Kutta-Fehlberg Method 282 ep Methods 289 5.7 Variable Step-Size Multistep Methods 301 5.8 Extrapolation Methods 307 5.9 Higher-Order Equations and Systems of Differential Equations 313 5.10 Stability 324 5.11 Stiff Differential equations 334 5.12 Survey of Methods and Software 342 6 Direct Methods for Solving near Systems 344 6.1 Linear Systems of Equations 345 6.2 Pivoting Strategies 359 6.3 Linear Algebra and Matrix Inversion 370 6.4 The determinant of a Matrix 383 6.5 Matrix Factorization 388 6.6 Special Types of Matrices 398 6. 7 Survey of Methods and Software 413 Contents 7 Iterative Techniques in Matrix algebra 417 7.1 Norms of vectors and matrices 418 7,2 Eigenvalues and Eigenvectors 430 7.3 Iterative Techniques for Solving Linear Systems 437 7. 4 Error Bounds and iterative Refinement 454 7.5 The Conjugate Gradient Method 465 7.6 Survey of Methods and Software 481 8 Approximation Theory 483 8.1 Discrete Least Squares Approximation 484 8.2 Orthogonal Polynomials and Least Squares approximation 498 8.3 Chebyshev Polynomials and Economization of Power Series 507 8.4 Rational Function Approximation 517 8.5 Trigonometric Polynomial Approximation 529 8.6 Fast Fourier Transforms 537 8.7 Survey of Methods and Software 548 9 Approximating Eigenvalues 550 9. 1 Linear algebra and eigenvalues 551 9.2 The Power Method 560 9.3 Householder's Method 577 9. 4 The OR Algorithm 58 9.5 Survey of Methods and Software 597 10 Numerical Solutions of Nonlinear systems 10.1 Fixed Points for Functions of s 10.2 Newton's Method 611 10.3 Quasi-Newton Methods 620 10.4 Steepest Descent Techniques 628 10.5 Homotopy and Continuation Methods 635 10.6 Survey of Methods and Software 643 Contents 1 Boundary-Value Problems for ordinary Differential Equations 645 11. 1 The Linear Shooting Method 646 11.2 The Shooting Method for Nonlinear Problems 653 11.3 Finite-Difference Methods for linear problens 660 11.4 Finite-Difference methods for Nonlinear Problems 667 11. 5 The Rayleigh-Ritz Method 672 11.6 Survey of Methods and Software 688 Numerical solutions to partial Differential Equations 691 12. 1 Elliptic Partial Differential Equations 694 12.2 Parabolic Partial Differential Equations 704 12.3 Hyperbolic Partial Differential Equations 718 12. 4 An Introduction to the Finite-Element Method 726 12.5 Survey of Methods and software 741 Bibliography 743 Answers to selected exercises 753 Index 837 CHAPTER 1 Mathematical Preliminaries beginning chemistry courses, we see the ideal gas law PYE NRT which relates the pressure P, volume V, temperature T, and number of moles n of anideal"gas. In this equation, R is a constant that depends on the measurement system. Suppose two experiments are conducted to test this law, using the same gas in each case. In the first experiment, P=1.00 atn V=0100 N=0.00420mol,R=0.083206, The ideal gas law predicts the temperature of the gas to be 1.00)(0.1 T =290.15K=17C NR(0.004200.08206 When we measure the temperature of the gas, we find that the true tem perature is 15°C. Vi v2

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2014-12-25
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