E-Book, Englisch, 388 Seiten, Web PDF
Vandergraft / Rheinboldt Introduction to Numerical Computations
2. Auflage 2014
ISBN: 978-1-4832-6709-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 388 Seiten, Web PDF
ISBN: 978-1-4832-6709-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Computer Science and Applied Mathematics: Introduction to Numerical Computations, Second Edition introduces numerical algorithms as they are used in practice. This edition covers the usual topics contained in introductory numerical analysis textbooks that include all of the well-known and most frequently used algorithms for interpolation and approximation, numerical differentiation and integration, solution of linear systems and nonlinear equations, and solving ordinary differential equations. A complete discussion of computer arithmetic, problems that arise in the computer evaluation of functions, and cubic spline interpolation are also provided. This text likewise discusses the Newton formulas for interpolation and adaptive methods for integration. The level of this book is suitable for advanced undergraduate students and readers with elementary mathematical background.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Introduction to Numerical Computations;4
3;Copyright Page;5
4;Dedication;6
5;Table of Contens;8
6;PREFACE;10
7;ACKNOWLEDGMENTS;12
8;LIST OF SPECIAL SYMBOLS;14
9;Chapter 1. BASIC ASPECTS OF NUMERICAL COMPUTATIONS;16
9.1;1.1 Numerical Algorithms;16
9.2;1.2 Unstable Problems (Ill-Conditioning);23
9.3;1.3 Unstable Methods;26
9.4;Suggestions for Further Reading;32
10;Chapter 2. COMPUTER ARITHMETIC;33
10.1;2.1 Number Representation;33
10.2;2.2 Floating Point Numbers;37
10.3;2.3 Arithmetic Operations;45
10.4;2.4 Errors in Computer Arithmetic;55
10.5;2.5 Analysis of Errors;62
10.6;Suggestions for Further Reading;74
11;Chapter 3. EVALUATION OF FUNCTIONS;75
11.1;3.1 Summation;75
11.2;3.2 Polynomial Evaluation;83
11.3;3.3 Rational and Transcendental Functions;92
11.4;3.4 Avoiding Subtractive Cancellation;99
11.5;Suggestions for Further Reading;103
12;Chapter 4. INTERPOLATION AND APPROXIMATION;104
12.1;4.1 Polynomial Interpolation;104
12.2;4.2 Least Squares Approximation;127
12.3;4.3 Spline Interpolation;141
12.4;Suggestions for Further Reading;153
13;Chapter 5. DIFFERENTIATION AND INTEGRATION;154
13.1;5.1 Numerical Differentiation;154
13.2;5.2 Numerical Integration—Newton–Cotes Formulas;164
13.3;5.3 Adaptive Integration;176
13.4;5.4 Romberg Integration;186
13.5;5.5 Numetical Integration—Gaussian Methods;193
13.6;Suggestions for Further Reading;204
14;Chapter 6. SYSTEMS OF LINEAR EQUATIONS;205
14.1;6.1 Basic Concepts;205
14.2;6.2 Gaussian Elimination;210
14.3;6.3+ Matrix Applications of Gaussian Elimination;221
14.4;6.4 Rounding Error Analysis;231
14.5;6.5 Error Estimates and Accuracy Improvement;240
14.6;6.6 Efficiency Estimates;245
14.7;6.V Error Estimates—Matrix Methods;248
14.8;6.8 Iterative Methods;256
14.9;Suggestions for Further Reading;273
15;Chapter 7. NONLINEAR EQUATIONS;274
15.1;7.1 Basic Methods;274
15.2;7.2 Convergence Results;288
15.3;7.3 Stability and Effects of Rounding Errors;294
15.4;7.4 Efficiency—Rates of Convergence;303
15.5;7.5 Roots of Polynomials;311
15.6;Suggestions for Further Reading;325
16;Chapter 8. ORDINARY DIFFERENTIAL EQUATIONS;326
16.1;8.1 Differential and Difference Equations;326
16.2;8.2 Basic Methods;337
16.3;8.3 Error Estimates;349
16.4;8.4 Practical Aspects of Solving Differential Equations;363
16.5;8.5 Boundary Value Problems;369
16.6;Suggestions for Further Reading;376
17;APPENDIX;377
18;BIBLIOGRAPHY;379
19;INDEX;382
20;Computer Science and Applied Mathematics;388
