An introduction to numerical analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1989
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVI, 693 S. |
| ISBN: | 0471624896 0471500232 |
Staff View
MARC
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| 100 | 1 | |a Atkinson, Kendall E. |d 1940- |e Verfasser |0 (DE-588)12286977X |4 aut | |
| 245 | 1 | 0 | |a An introduction to numerical analysis |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Wiley |c 1989 | |
| 300 | |a XVI, 693 S. | ||
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| 500 | |a Literaturangaben | ||
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| 650 | 4 | |a Analyse numérique | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001196724 | ||
Record in the Search Index
| _version_ | 1804116268338380800 |
|---|---|
| adam_text | CONTENTS
ONE
ERROR: ITS SOURCES, PROPAGATION,
AND ANALYSIS 3
1.1 Mathematical Preliminaries 3
1.2 Computer Representation of Numbers 11
1.3 Definitions and Sources of Error 17
1.4 Propagation of Errors 23
1.5 Errors in Summation 29
1.6 Stability in Numerical Analysis 34
Discussion of the Literature 39
Problems 43
TWO
ROOTFINDING FOR NONLINEAR EQUATIONS 53
2.1 The Bisection Method 56
2.2 Newton s Method 58
2.3 The Secant Method 65
2.4 Muller s Method 73
2.5 A General Theory for One-Point Iteration Methods 76
2.6 Aitken Extrapolation for Linearly Convergent Sequences 83
2.7 The Numerical Evaluation of Multiple Roots 87
2.8 Brent s Rootfinding Algorithm 91
2.9 Roots of Polynomials 94
2.10 Systems of Nonlinear Equations 103
2.11 Newton s Method for Nonlinear Systems 108
2.12 Unconstrained Optimization 111
Discussion of the Literature 114
Problems H7
THREE
INTERPOLATION THEORY 131
3.1 Polynomial Interpolation Theory 131
3.2 Newton Divided Differences 138
xiv CONTENTS
3.3 Finite Differences and Table-Oriented Interpolation Formulas 147
3.4 Errors in Data and Forward Differences 151
3.5 Further Results on Interpolation Error 154
3.6 Hermite Interpolation 159
3.7 Piecewise Polynomial Interpolation 163
3.8 Trigonometric Interpolation 176
Discussion of the Literature 183
Problems 185
FOUR
APPROXIMATION OF FUNCTIONS 197
4.1 The Weierstrass Theorem and Taylor s Theorem 197
4.2 The Minimax Approximation Problem 201
4.3 The Least Squares Approximation Problem 204
4.4 Orthogonal Polynomials 207
4.5 The Least Squares Approximation Problem (continued) 216
4.6 Minimax Approximations 222
4.7 Near-Minimax Approximations 225
Discussion of the Literature 236
Problems 239
FIVE
NUMERICAL INTEGRATION 249
5.1 The Trapezoidal Rule and Simpson s Rule 251
5.2 Newton-Cotes Integration Formulas 263
5.3 Gaussian Quadrature 270
5.4 Asymptotic Error Formulas and Their Applications 284
5.5 Automatic Numerical Integration 299
5.6 Singular Integrals 305
5.7 Numerical Differentiation 315
Discussion of the Literature 320
Problems 323
SIX
NUMERICAL METHODS FOR ORDINARY
DIFFERENTIAL EQUATIONS 333
6.1 Existence, Uniqueness, and Stability Theory 335
6.2 Euler s Method 341
6.3 Multistep Methods 357
6.4 The Midpoint Method 361
6.5 The Trapezoidal Method 366
6.6 A Low-Order Predictor-Corrector Algorithm 373
CONTENTS XV
6.7 Derivation of Higher Order Multistep Methods 381
6.8 Convergence and Stability Theory for Multistep Methods 394
6.9 Stiff Differential Equations and the Method of Lines 409
6.10 Single-Step and Runge-Kutta Methods 418
6.11 Boundary Value Problems 433
Discussion of the Literature 444
Problems 450
SEVEN
LINEAR ALGEBRA 463
7.1 Vector Spaces, Matrices, and Linear Systems 463
7.2 Eigenvalues and Canonical Forms for Matrices 471
7.3 Vector and Matrix Norms 480
7.4 Convergence and Perturbation Theorems 490
Discussion of the Literature 495
Problems 496
EIGHT
NUMERICAL SOLUTION OF SYSTEMS
OF LINEAR EQUATIONS 507
8.1 Gaussian Elimination 508
8.2 Pivoting and Scaling in Gaussian Elimination 515
8.3 Variants of Gaussian Elimination 522
8.4 Error Analysis 529
8.5 The Residual Correction Method 540
8.6 Iteration Methods 544
8.7 Error Prediction and Acceleration 552
8.8 The Numerical Solution of Poisson s Equation 557
8.9 The Conjugate Gradient Method 562
Discussion of the Literature 569
Problems 574
NINE
THE MATRIX EIGENVALUE PROBLEM 587
9.1 Eigenvalue Location, Error, and Stability Results 588
9.2 The Power Method 602
9.3 Orthogonal Transformations Using Householder Matrices 609
9.4 The Eigenvalues of a Symmetric Tridiagonal Matrix 619
9.5 The QR Method 623
9.6 The Calculation of Eigenvectors and Inverse Iteration 628
9.7 Least Squares Solution of Linear Systems 633
Discussion of the Literature 645
Problems 648
xvi CONTENTS
APPENDIX:
MATHEMATICAL SOFTWARE 661
ANSWERS TO SELECTED EXERCISES 667
INDEX 683
|
| any_adam_object | 1 |
| author | Atkinson, Kendall E. 1940- |
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| ctrlnum | (OCoLC)17551990 (DE-599)BVBBV001775703 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001775703 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:35:48Z |
| institution | BVB |
| isbn | 0471624896 0471500232 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001196724 |
| oclc_num | 17551990 |
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| physical | XVI, 693 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Wiley |
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| spelling | Atkinson, Kendall E. 1940- Verfasser (DE-588)12286977X aut An introduction to numerical analysis 2. ed. New York u.a. Wiley 1989 XVI, 693 S. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Analise Numerica larpcal Analyse numérique Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Atkinson, Kendall E. 1940- An introduction to numerical analysis Analise Numerica larpcal Analyse numérique Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | An introduction to numerical analysis |
| title_auth | An introduction to numerical analysis |
| title_exact_search | An introduction to numerical analysis |
| title_full | An introduction to numerical analysis |
| title_fullStr | An introduction to numerical analysis |
| title_full_unstemmed | An introduction to numerical analysis |
| title_short | An introduction to numerical analysis |
| title_sort | an introduction to numerical analysis |
| topic | Analise Numerica larpcal Analyse numérique Numerieke wiskunde gtt Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analise Numerica Analyse numérique Numerieke wiskunde Numerical analysis Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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