Rice Numerical Methods in Software and Analysis

2. Auflage 2014
ISBN: 978-1-4832-9568-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 720 Seiten, Web PDF

Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms. The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. - Emphasizes the use of high-quality mathematical software for numerical computation - Extensive use of IMSL routines - Features extensive examples and case studies

Autoren/Hrsg.

Rice, John R.

Inhaltsverzeichnis

1;Front Cover;1
2;Numerical Methods, Software, and Analysis;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;12
6;CHAPTER 1. MATHEMATICS AND COMPUTER SCIENCE BACKGROUND;16
6.1;1.1 Calculus;16
6.2;1.2 Vectors, Matrices, and Linear Equations;20
6.3;1.3 Differential Equations;25
6.4;1.4 Programming;27
7;CHAPTER 2. NUMERICAL SOFTWARE;34
7.1;2.1 The Library Concept;35
7.2;2.2 Using a Library;36
7.3;2.3 Standard Numerical Software;39
7.4;2.4 The IMSL Mathematics Library;45
7.5;2.5 The PROTRAN System;47
8;CHAPTER 3. ERRORS, ROUND-OFF, AND STABILITY;54
8.1;3.1 Sources of Uncertainty;54
8.2;3.2 Numerical Approximations;56
8.3;3.3 Round-Off Errors;64
8.4;3.4 Case Study: Calculation of p;77
8.5;3.5 How to Estimate Errors and Uncertainty;82
9;CHAPTER 4. MODELS AND FORMULAS FOR NUMERICAL COMPUTATION;84
9.1;4.1 Polynomials;84
9.2;4.2 Piecewise Polynomials;87
9.3;4.3 Splines;90
9.4;4.4 Other Piecewise Polynomials and Splines with Multiple Knots;97
9.5;4.5 General Methods for Deriving Formulas;100
10;CHAPTER 5. INTERPOLATION;108
10.1;5.1 General Interpolation Using Linear Equation Solvers;108
10.2;5.2 Interpolation Methods for Polynomials;111
10.3;5.3 Interpolation Methods for Piecewise Polynomials;123
10.4;5.4 Software for Interpolation;128
10.5;5.5 Choice of Interpolation Forms and Points;157
10.6;5.6 Error Analysis for Interpolation;174
11;CHAPTER 6. MATRICES AND LINEAR EQUATIONS;188
11.1;6.1 Types and Sources of Matrix Computation Problems;188
11.2;6.2 Gauss Elimination, Lu-Factorization, and Pivoting;196
11.3;6.3 Iteration Methods for Linear Systems;211
11.4;6.4 Software for Linear Equations;216
11.5;6.5 Case Study: Design of the Interface for a Linear Equations Solver;240
11.6;6.6 Analysis of the Linear Equations Problem;244
11.7;6.7 Eigensystem Problems and Software;262
12;CHAPTER 7. DIFFERENTIATION AND INTEGRATION;278
12.1;7.1 Methods for Estimating Derivatives;278
12.2;7.2 Software for Differentiation;281
12.3;7.3 Error Analysis for Differentiation;284
12.4;7.4 The Estimation of Integrals;287
12.5;7.5 Adaptive Quadrature;295
12.6;7.6 Software for Integration;304
12.7;7.7 Error Analysis for Integration;333
13;CHAPTER 8. NONLINEAR EQUATIONS;338
13.1;8.1 Formulating Problems as F(X)=0;338
13.2;8.2 Methods for One Nonlinear Equation;342
13.3;8.3 Special Situations and Polyalgorithms;360
13.4;8.4 Polynomial Equations;365
13.5;8.5 Systems of Nonlinear Equations;368
13.6;8.6 Software for Nonlinear Equations;378
13.7;8.7 Analysis of Methods for Nonlinear Equations;406
13.8;8.8 Selection of Methods for Nonlinear Equations;417
14;CHAPTER 9. ORDINARY DIFFERENTIAL EQUATIONS;426
14.1;9.1 Introduction;426
14.2;9.2 Basic Methods for Initial Value Problems;433
14.3;9.3 Polyalgorithms for Differential Equations;446
14.4;9.4 Systems of Differential Equations;455
14.5;9.5 Software for Differential Equations;457
14.6;9.6 Analysis of Methods for Differential Equations;490
15;CHAPTER 10. PARTIAL DIFFERENTIAL EQUATIONS;500
15.1;10.1 Partial Differential Equations as Physical Models;500
15.2;10.2 Discretization Methods;505
15.3;10.3 Solution of the System of Algebraic Equations;547
15.4;10.4 Software for Partial Differential Equations;554
16;CHAPTER 11. APPROXIMATION OF FUNCTIONS AND DATA;566
16.1;11.1 Approximation Problems;566
16.2;11.2 Least Squares and Regression;572
16.3;11.3 L1 and Chebyshev Approximation;586
16.4;11.4 Software for Approximation;588
16.5;11.5 Case Study: The Representation of Data;603
16.6;11.6 Case Study: The Smoothing of Data;620
16.7;11.7 Approximation of Mathematical Functions;636
16.8;11.8 Orthogonal Polynomials;642
17;CHAPTER 12. SOFTWARE PRACTICE, COSTS, AND ENGINEERING;648
17.1;12.1 Software Types and Life Cycles;649
17.2;12.2 Programming Environment and Practice;652
17.3;12.3 Software Quality and Costs;662
17.4;12.4 Software Parts and Very High Level Languages;668
18;CHAPTER 13. SOFTWARE PERFORMANCE EVALUATION;674
18.1;13.1 Program Efficiency;675
18.2;13.2 Software Reliability and Robustness;682
18.3;13.3 Software Portability;684
18.4;13.4 Reporting Computational Experiments;689
19;CHAPTER 14. THE VALIDATION OF NUMERICAL COMPUTATIONS;692
19.1;14.1 Validation of Models in Numerical Computation;693
19.2;14.2 Sensitivity Analysis and Error Estimation;694
19.3;14.3 Software Errors;697
20;CHAPTER 15. PROTRAN;700
20.1;15.1 How PROTRAN Works;700
20.2;15.2 PROTRAN Variables: Scalars, Vectors, and Matrices;702
20.3;15.3 Debugging PROTRAN Programs;709
20.4;15.4 PROTRAN Statements;710
21;INDEX;720