Principles and procedures of numerical analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Plenum Press
1978
|
| Schriftenreihe: | Mathematical concepts and methods in science and engineering
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 331 S. |
| ISBN: | 0306400871 |
Internformat
MARC
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| 245 | 1 | 0 | |a Principles and procedures of numerical analysis |c Ferenc Szidarovszky and Sidney Yakowitz |
| 264 | 1 | |a New York [u.a.] |b Plenum Press |c 1978 | |
| 300 | |a XII, 331 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical concepts and methods in science and engineering |v 14 | |
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Numerical analysis | |
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| 700 | 1 | |a Yakowitz, Sidney J. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematical concepts and methods in science and engineering |v 14 |w (DE-604)BV000001144 |9 14 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001484238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804116715624202240 |
|---|---|
| adam_text | Contents
1. Preliminaries 1
1.1. Number Systems and Representations of Numbers 1
1.2. Error Analysis 9
1.2.1. Upper Bounds in Arithmetic 10
1.2.2. Probabilistic Error Analysis 18
1.2.3. Propagation of Errors 19
1.3. Supplementary Notes and Discussion 23
2. Approximation and Interpolation of Functions 25
2.1. Interpolating Polynomials 29
2.1.1. Lagrange Interpolating Polynomials 29
2.1.2. Error Bounds for Interpolating Polynomials 31
2.1.3. Differences 35
2.1.4. The Fraser Diagram 38
2.1.5. Aitken s Method and Computational Requirements of
Interpolation 46
2.1.6. Hermite Interpolation 48
2.1.7. Inverse Interpolation 49
2.2. Uniform Approximations 49
2.3. Least Squares Approximation 53
2.4. Spline Functions 59
2.5. Asymptotic Properties of Polynomial Approximations 63
2.6. Supplementary Notes and Discussion 69
3. Numerical Differentiation and Integration 73
3.1. Numerical Differentiation 75
3.2. Numerical Quadrature 79
ix
x Contents
3.2.1. Interpolatory Quadrature Formulas 79
3.2.2. Error Analysis and Richardson Extrapolation 81
3.2.3. Gaussian Quadrature 88
3.2.4. The Euler Maclaurin Formula 97
3.2.5. Romberg Integration 105
3.3. Supplementary Notes and Discussion 107
4. General Theory for Iteration Methods Ill
4.1. Metric Spaces 112
4.2. Examples of Metric Spaces 114
4.3. Operators on Metric Spaces 117
4.4. Examples of Bounded Operators 118
4.5. Iterations of Operators 121
4.6. Fixed Point Theorems 124
4.7. Systems of Operator Equations 131
4.8. Norms of Vectors and Matrices 134
4.9. The Order of Convergence of an Iteration Process 137
4.10. Inner Products 138
4.11. Supplementary Notes and Discussion 139
5. Solution of Nonlinear Equations 141
5.1. Equations in One Variable 141
5.1.1. The Bisection Method 141
5.1.2. The Method of False Position (Regula Falsi) 143
5.1.3. The Secant Method 147
5.1.4. Newton s Method 149
5.1.5. Application of Fixed Point Theory 154
5.1.6. Acceleration of Convergence, and Aitken s 52 Method ... 158
5.2. Solution of Polynomial Equations 160
5.2.1. Sturm Sequences 161
5.2.2. The Lehmer Schur Method 163
5.2.3. Bairstow s Method 165
5.2.4. The Effect of Coefficient Errors on the Roots 167
5.3. Systems of Nonlinear Equations and Nonlinear Programming ... 169
5.3.1. Iterative Methods for Solution of Systems of Equations ... 170
5.3.2. The Gradient Method and Related Techniques 174
5.4. Supplementary Notes and Discussion 178
6. The Solution of Simultaneous Linear Equations 179
6.1. Direct Methods 180
6.1.1. Gaussian Elimination 180
6.1.2. Variants of Gaussian Elimination 186
6.1.3. Inversion by Partitioning 192
6.2. Iteration Methods 195
6.2.1. Stationary Iteration Processes 196
Contents xi
6.2.2. Iteration Processes Based on the Minimization of Quadratic
Forms 201
6.2.3. Application of the Gradient Method 206
6.2.4. The Conjugate Gradient Method 207
6.3. Matrix Conditioning and Error Analysis 212
6.3.1. Bounds for Errors of Perturbed Linear Equations 212
6.3.2. Error Bounds for Rounding in Gaussian Elimination .... 216
6.4. Supplementary Notes and Discussion 219
7. The Solution of Matrix Eigenvalue Problems 221
7.1. Preliminaries 222
7.1.1. Some Matrix Algebra Background 222
7.1.2. The Householder Transformation and Reduction to
Hessenberg Form 230
7.1.3. Matrix Deflation 234
7.2. Some Basic Eigenvalue Approximation Methods 234
7.2.1. The Power Method 236
7.2.2. The Inverse Power Method 239
7.2.3. The Rayleigh Quotient Iteration Method 240
7.2.4. Jacobi Type Methods 245
7.3. The QR Algorithm 248
7.3.1. Principles and Convergence Rates 248
7.3.2. Implementation of the QR Algorithm 250
7.4. Eigenproblem Error Analysis 252
7.5. Supplementary Notes and Discussion 255
8. The Numerical Solution of Ordinary Differential Equations . . . 257
8.1. The Solution of Initial Value Problems 259
8.1.1. Picard s Method of Successive Approximation 259
8.1.2. The Power Series Method 260
8.1.3. Methods of the Runge Kutta Type 263
8.1.4. Linear Multistep Methods 272
8.1.5. Step Size and Its Adaptive Selection 278
8.1.6. The Method of Quasilinearization 280
8.2. The Solution of Boundary Value Problems 284
8.2.1. Reduction to Initial Value Problems 284
8.2.2. The Method of Undetermined Coefficients 285
8.2.3. The Difference Method 287
8.2.4. The Method of Quasilinearization 289
8.3. The Solution of Eigenvalue Problems 290
8.4. Supplementary Notes and Discussion 292
9. The Numerical Solution of Partial Differential Equations .... 295
9.1. The Difference Method 296
9.2. The Method of Quasilinearization 303
xii Contents
9.3. The Ritz Galerkin Finite Element Approach 304
9.3.1. The Ritz Method 304
9.3.2. The Galerkin Method 310
9.3.3. The Finite Element Method 311
9.4. Supplementary Notes and Discussion 318
References 321
Index 327
|
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| id | DE-604.BV002258564 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:55Z |
| institution | BVB |
| isbn | 0306400871 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001484238 |
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| physical | XII, 331 S. |
| publishDate | 1978 |
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| publisher | Plenum Press |
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| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Szidarovszky, Ferenc 1945- Verfasser (DE-588)121012158 aut Principles and procedures of numerical analysis Ferenc Szidarovszky and Sidney Yakowitz New York [u.a.] Plenum Press 1978 XII, 331 S. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 14 Analyse numérique Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Yakowitz, Sidney J. Verfasser aut Mathematical concepts and methods in science and engineering 14 (DE-604)BV000001144 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001484238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Szidarovszky, Ferenc 1945- Yakowitz, Sidney J. Principles and procedures of numerical analysis Mathematical concepts and methods in science and engineering Analyse numérique Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Principles and procedures of numerical analysis |
| title_auth | Principles and procedures of numerical analysis |
| title_exact_search | Principles and procedures of numerical analysis |
| title_full | Principles and procedures of numerical analysis Ferenc Szidarovszky and Sidney Yakowitz |
| title_fullStr | Principles and procedures of numerical analysis Ferenc Szidarovszky and Sidney Yakowitz |
| title_full_unstemmed | Principles and procedures of numerical analysis Ferenc Szidarovszky and Sidney Yakowitz |
| title_short | Principles and procedures of numerical analysis |
| title_sort | principles and procedures of numerical analysis |
| topic | Analyse numérique Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique Numerical analysis Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001484238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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