E-Book, Englisch, 214 Seiten, Web PDF
Ortega / Rheinboldt Numerical Analysis
1. Auflage 2014
ISBN: 978-1-4832-6850-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
A Second Course
E-Book, Englisch, 214 Seiten, Web PDF
ISBN: 978-1-4832-6850-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Computer Science and Applied Mathematics: Numerical Analysis: A Second Course presents some of the basic theoretical results pertaining to the three major problem areas of numerical analysis-rounding error, discretization error, and convergence error. This book is organized into four main topics: mathematical stability and ill conditioning, discretization error, convergence of iterative methods, and rounding error. In these topics, this text specifically discusses the systems of linear algebraic equations, eigenvalues and eigenvectors, and differential and difference equations. The discretization error for initial and boundary value problems, systems of linear and nonlinear equations, and rounding error for Gaussian elimination are also elaborated. This publication is recommended for undergraduate level students and students taking a one-semester first-year graduate course for computer science and mathematics majors.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Numerical Analysis: A Second Course;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;LIST OF COMMONLY USED SYMBOLS;14
8;INTRODUCTION;16
9;CHAPTER I. LINEAR ALGEBRA;20
9.1;I.I EIGENVALUES AND CANONICAL FORMS;20
9.2;1.2 VECTOR NORMS;30
9.3;1.3 MATRIX NORMS;35
9.4;READING;42
10;PART I: MATHEMATICALSTABILITY AND ILL CONDITIONING;44
10.1;CHAPTER 2. SYSTEMS OF LINEARALGEBRAIC EQUATIONS;46
10.1.1;2.1 BASIC ERROR ESTIMATES AND CONDITION NUMBERS;46
10.1.2;2.2 A POSTERIORI BOUNDS AND EIGENVECTOR COMPUTATIONS;53
10.1.3;READING;56
10.2;CHAPTER 3. EIGENVALUES AND EIGENVECTORS;57
10.2.1;3.1 CONTINUITY RESULTS;57
10.2.2;3.2 THE GERSCHGORIN AND BAUER-FIKE THEOREMS;62
10.2.3;3.3 SPECIAL RESULTS FOR SYMMETRIC MATRICES;71
10.2.4;READING;78
10.3;CHAPTER 4. DIFFERENTIAL ANDDIFFERENCE EQUATIONS;79
10.3.1;4.1 DIFFERENTIAL EQUATIONS;79
10.3.2;4.2 DIFFERENCE EQUATIONS;85
10.3.3;READING;93
11;PART II: DISCRETIZATION ERROR;94
11.1;CHAPTER 5. DISCRETIZATION ERRORFOR INITIAL VALUE PROBLEMS;96
11.1.1;5.1 CONSISTENCY AND STABILITY;96
11.1.2;5.2 CONVERGENCE AND ORDER;103
11.1.3;READING;110
11.2;CHAPTER 6. DISCRETIZATION ERROR FOR BOUNDARY VALUE PROBLEMS;111
11.2.1;6.1 THE MAXIMUM PRINCIPLE;111
11.2.2;6.2 MATRIX METHODS;117
11.2.3;READING;129
12;PART III: CONVERGENCE OF ITERATIVE METHODS;130
12.1;CHAPTER 7. SYSTEMS OF LINEAR EQUATIONS;132
12.1.1;7.1 CONVERGENCE;132
12.1.2;7.2 RATE OF CONVERGENCE;140
12.1.3;7.3 APPLICATIONS TO DIFFERENTIAL EQUATIONS;150
12.1.4;READING;154
12.2;CHAPTER 8. SYSTEMS OF NONLINEAR EQUATIONS;155
12.2.1;8.1 LOCAL CONVERGENCE AND RATE OF CONVERGENCE;155
12.2.2;8.2 ERROR ESTIMATES;167
12.2.3;8.3 GLOBAL CONVERGENCE;176
12.2.4;READING;181
13;PART IV: ROUNDING ERROR;182
13.1;CHAPTER 9. ROUNDING ERRORFOR GAUSSIAN ELIMINATION;184
13.1.1;9.1 REVIEW OF THE METHOD;184
13.1.2;9.2 ROUNDING ERROR AND INTERCHANGE STRATEGIES;190
13.1.3;9.3 BACKWARD ERROR ANALYSIS;197
13.1.4;9.4 ITERATIVE REFINEMENT;204
13.1.5;READING;208
14;BIBLIOGRAPHY;210
15;INDEX;212
