Elementary numerical analysis: an algorithmic approach
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1972
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | International series in pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 396 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Elementary numerical analysis |b an algorithmic approach |c S. D. Conte ; Carl de Boor |
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| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1972 | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface vii
Introduction ix
1. Number Systems and Errors 1
1.1 The Representation of Integers 1
1.2 The Representation of Fractions 4
1.3 Floating-point Arithmetic 7
1.4 Error Propagation; Significance Errors and Instability 10
7.5 Computational Methods for Error Estimation 15
1.6 Some Comments on Convergence of Sequences 17
1.7 Some Mathematical Preliminaries 21
2. The Solution of Nonlinear Equations 27
2.1 A Survey of Iterative Methods 28
2.2 FORTRAN Programs for Some Iterative Methods 35
2.3 Fixed-point Iteration 44
2.4 Convergence Acceleration for Fixed-point Iteration 50
2.5 Quadratic Convergence and Newton s Method 57
2.6 Polynomial Equations: Real Roots 66
2.7 Complex Roots and Muller s Method 74
2.8 Simultaneous Nonlinear Equations 84
3. Matrices and Systems of Linear Equations 91
3.1 Properties of Matrices 91
3.2 The Solution of Linear Systems by Elimination 110
3.3 The Pivoting Strategy 123
3.4 The Triangular Factorization and Calculation of the Inverse 127
*3.5 Compact Schemes 137
3.6 Error and Residual of an Approximate Solution; Norms 142
3.7 The Condition Number and Iterative Imr ovement 150
3.8 Iterative Methods 157
3.9 Eigenvalues and the Convergence of Fixed-point Iteration 170
3.10 Determinants 180
3.11 The Eigenvalue Problem 184
vi CONTENTS
4. Interpolation and Approximation 191
4.1 The Interpolating Polynomial: Lagrange Form 191
4.2 The Interpolating Polynomial: Newton Form 195
4.3 The Divided-difference Table 201
4.4 The Error of the Interpolating Polynomial 210
4.5 Interpolation in a Function Table Based on Equally Spaced Points 213
4.6 The Divided Difference as a Function of Its Arguments and
Osculatory Interpolation 221
4.7 The Case for Piecewise-polynomial Interpolation 230
*4.8 Piecewise-cubic Interpolation 233
4.9 Data Fitting 241
*4.10 Orthogonal Polynomials 246
*4.11 Least-squares Approximation by Polynomials 255
*4.12 Chebyshev Economization 265
5. Differentiation and Integration 274
5./ Numerical Differentiation 275
5.2 Numerical Integration: Some Basic Rules 284
5.3 Numerical Integration: Composite Rules 290
5.4 Numerical Integration: Gaussian Rules 299
5.5 Extrapolation to the Limit; Romberg Integration 307
6. The Solution of Differential Equations 319
6.1 Mathematical Preliminaries 320
6.2 Simple Difference Equations 322
6.3 Numerical Integration by Taylor Series 327
6.4 Error Estimates and Convergence of Euler s Method 332
6.5 Runge-Kutta Methods 336
6.6 Multistep Formulas 340
6.7 Predictor-Corrector Methods 346
6.8 The Adams-Moulton Method 350
6.9 Stability of Numerical Methods 357
6.10 Round-off-error Propagation 361
6.11 Systems of Differential Equations 365
7. Boundary-value Problems in Ordinary Differential Equations 373
7.1 Finite-difference Methods: Second-order Equations 374
7.2 Finite-difference Methods: Fourth-order Equations 379
7.3 Shooting Methods 382
References 388
Index 391
I
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| physical | X, 396 S. |
| publishDate | 1972 |
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| series2 | International series in pure and applied mathematics |
| spelling | Conte, Samuel D. Verfasser aut Elementary numerical analysis an algorithmic approach S. D. Conte ; Carl de Boor 2. ed. New York [u.a.] McGraw-Hill 1972 X, 396 S. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Analyse numérique Matematica larpcal Sayısal analiz - Bilgi işlem Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s DE-604 De Boor, Carl 1937- Verfasser (DE-588)109311507 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conte, Samuel D. De Boor, Carl 1937- Elementary numerical analysis an algorithmic approach Analyse numérique Matematica larpcal Sayısal analiz - Bilgi işlem Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4123623-3 |
| title | Elementary numerical analysis an algorithmic approach |
| title_auth | Elementary numerical analysis an algorithmic approach |
| title_exact_search | Elementary numerical analysis an algorithmic approach |
| title_full | Elementary numerical analysis an algorithmic approach S. D. Conte ; Carl de Boor |
| title_fullStr | Elementary numerical analysis an algorithmic approach S. D. Conte ; Carl de Boor |
| title_full_unstemmed | Elementary numerical analysis an algorithmic approach S. D. Conte ; Carl de Boor |
| title_short | Elementary numerical analysis |
| title_sort | elementary numerical analysis an algorithmic approach |
| title_sub | an algorithmic approach |
| topic | Analyse numérique Matematica larpcal Sayısal analiz - Bilgi işlem Datenverarbeitung Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique Matematica Sayısal analiz - Bilgi işlem Datenverarbeitung Numerical analysis Data processing Numerische Mathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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