Numerical analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. u.a.
Addison-Wesley
1982
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 563 S. graph. Darst. |
| ISBN: | 0201103923 |
Internformat
MARC
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| 100 | 1 | |a Johnson, Lee W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis |c Lee W. Johnson ; Ronald D. Riess* |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Reading, Mass. u.a. |b Addison-Wesley |c 1982 | |
| 300 | |a XII, 563 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Analyse numérique | |
| 650 | 7 | |a EDP |2 inriac | |
| 650 | 7 | |a analyse numérique |2 inriac | |
| 650 | 7 | |a approximation |2 inriac | |
| 650 | 7 | |a dérivation numérique |2 inriac | |
| 650 | 7 | |a interpolation |2 inriac | |
| 650 | 7 | |a intégration numérique |2 inriac | |
| 650 | 7 | |a optimisation |2 inriac | |
| 650 | 7 | |a problème valeur propre |2 inriac | |
| 650 | 7 | |a système équation linéaire |2 inriac | |
| 650 | 7 | |a équation différentielle ordinaire |2 inriac | |
| 650 | 7 | |a équation non linéaire |2 inriac | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
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| 700 | 1 | |a Riess, Ronald Dean |d 1940- |e Verfasser |4 aut | |
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| 940 | 1 | |q TUB-nveb | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001508570 | ||
Datensatz im Suchindex
| _version_ | 1804116755749011456 |
|---|---|
| adam_text | Contents
1 Computational and Mathematical Preliminaries
1.1 Introduction 1
1.2 Errors in computations 2
1.3 Rounding errors and floating point arithmetic 3
1.4 Review of fundamental mathematical results 13
2 Solution of Linear Systems of Equations
2.1 Introduction 16
2.2 Direct methods 22
2.2.1 Gauss elimination 23
2.2.2 Operations counts 26
2.2.3 Pivoting and scaling in Gauss elimination 27
2.2.4 Implementation of Gauss elimination and L[/ decomposition 32
2.3 Error analysis and norms 43
2.3.1 Vector norms 44
2.3.2 Matrix norms 47
2.3.3 Condition numbers and error estimates 49
2.3.4 Iterative improvement 55
2.4 Iterative methods 60
2.4.1 Basic iterative methods 62
2.4.2 Implementation of iterative methods 68
2.5 Least squares solution of overdetermined linear systems 71
*2.6 The Cauchy Schwarz inequality 75
3 The Algebraic Eigenvalue Problem
3.1 Introduction 78
3.2 The power method 84
3.2.1 The inverse power method 93
3.2.2 Localization of eigenvalues 98
3.2.3 Deflation 100
*3.2.4 The Rayleigh quotient iteration 103
3.3 Transformation methods 106
3.3.1 Reduction to Hessenberg form 109
ix
x Contents
3.3.2 Householder transformations 118
*3.4 Schur s theorem and related topics 134
4 Solution of Nonlinear Equations
4.1 Introduction 142
4.2 Bracketing methods 145
4.3 Fixed point methods 150
4.3.1 The fixed point problem 151
4.3.2 Rate of convergence of the fixed point algorithm 156
4.3.3 Newton s method 160
4.3.4 The secant method 166
4.3.5 Newton s method in two variables 169
4.4 Zeros of polynomials 172
4.4.1 Efficient evaluation of a polynomial and its derivatives 174
4.4.2 Bairstow s method 181
4.4.3 Localization of polynomial zeros 185
4.4.4 The inverse power method for polynomials 190
*4.5 Newton s method in several variables 194
5 Interpolation and Approximation
5.1 Introduction 202
5.2 Polynomial interpolation 207
5.2.1 Divided differences and the Newton form of the interpolating
polynomial 209
5.2.2 Interpolation at equally spaced points 216
5.2.3 Error of polynomial interpolation 224
5.2.4 Translating the interval 230
*5.2.5 Polynomial interpolation with derivative data 234
5.2.6 Interpolation by cubic splines 237
5.2.7 Interpolation in several variables and bicubic splines 248
5.3 Orthogonal polynomials and least squares approximations 255
5.3.1 Efficient computation of least squares approximations 267
*5.3.2 Error estimates for least squares approximations 273
5.3.3 B splines and the Rayleigh Ritz procedure 278
*5.4 Approximation by rational functions 284
6 Numerical Integration and Differentiation
6.1 Introduction 289
6.2 Interpolatory numerical integration 289
6.2.1 Transforming quadrature formulas to other intervals 294
6.2.2 Newton Cotes formulas 294
6.2.3 Errors of quadrature formulas 298
6.2.4 Composite rules for numerical integration 301
6.2.5 Multiple integrals 307
6.2.6 The Euler Maclaurin summation formula 309
6.3 Adaptive quadrature 313
Contents xi
6.4 Richardson extrapolation and numerical differentiation 319
6.4.1 Romberg integration 323
6.5 Gaussian quadrature 324
6.5.1 Interpolation at the zeros of orthogonal polynomials 331
6.5.2 Interpolation using Chebyshev polynomials 334
6.5.3 Clenshaw Curtis quadrature 337
6.6 Trigonometric polynomials and the fast Fourier transform 341
6.6.1 Least squares fits and interpolation at equally spaced points 344
*6.6.2 The fast Fourier transform 346
7 Numerical Solution of Ordinary Differential Equations
7.1 Introduction 350
7.2 One step methods 357
7.2.1 Euler s method 358
7.2.2 Taylor s series methods of order k 361
7.2.3 Runge Kutta methods 366
7.2.4 Variable step Runge Kutta methods 372
7.2.5 Implementation of variable step Runge Kutta methods 378
7.3 Convergence and error analysis for one step methods 389
7.4 «th order differential equations and systems of differential equations 394
7.5 Linear multistep methods 399
7.5.1 Adams methods and their implementation as predictor
corrector methods 402
7.5.2 Linear difference equations 411
7.5.3 Order and convergence for multistep methods 414
7.5.4 Relative stability for multistep methods 419
7.6 Absolute stability for one step methods and multistep methods; stiff
equations 424
7.6.1 Absolute stability for one step methods 425
7.6.2 Absolute stability for multistep methods 429
7.6.3 Stability considerations for systems of equations and the
problem of stiffness 431
7.7 The method of collocation 437
7.8 Boundary value problems for ordinary differential equations 441
7.8.1 Finite difference methods 441
7.8.2 Shooting methods 443
7.8.3 Collocation methods 445
8 Numerical Solution of Partial Differential Equations
8.1 Introduction 447
8.2 Parabolic equations 450
8.2.1 Implicit methods 453
8.2.2 Derivative boundary conditions 461
8.2.3 The two dimensional heat equation 463
8.3 Elliptic equations 469
8.3.1 Iterative methods for solving large systems 472
xii Contents
8.3.2 Mixed boundary data and irregular regions 481
8.4 Hyperbolic equations 484
8.5 Finite element techniques 487
8.5.1 The Rayleigh Ritz method 487
8.5.2 The Galerkin method 495
Appendix: Optimization
A.I Introduction 505
A.2 Extension of results from calculus 505
A.3 Descent methods 509
A.3.1 Steepest descent 510
A.3.2Quasi Newton methods 514
A.4 Lagrange multipliers 518
A.5 Linear programming 524
Answers to Selected Exercises 531
References 551
Index 555
|
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| dewey-full | 519.4 |
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| dewey-raw | 519.4 |
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| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| institution | BVB |
| isbn | 0201103923 |
| language | English |
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| physical | XII, 563 S. graph. Darst. |
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| spelling | Johnson, Lee W. Verfasser aut Numerical analysis Lee W. Johnson ; Ronald D. Riess* 2. ed. Reading, Mass. u.a. Addison-Wesley 1982 XII, 563 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse numérique EDP inriac analyse numérique inriac approximation inriac dérivation numérique inriac interpolation inriac intégration numérique inriac optimisation inriac problème valeur propre inriac système équation linéaire inriac équation différentielle ordinaire inriac équation non linéaire inriac Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Numerische Mathematik (DE-588)4042805-9 s DE-604 Riess, Ronald Dean 1940- Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001508570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Johnson, Lee W. Riess, Ronald Dean 1940- Numerical analysis Analyse numérique EDP inriac analyse numérique inriac approximation inriac dérivation numérique inriac interpolation inriac intégration numérique inriac optimisation inriac problème valeur propre inriac système équation linéaire inriac équation différentielle ordinaire inriac équation non linéaire inriac Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4151278-9 |
| title | Numerical analysis |
| title_auth | Numerical analysis |
| title_exact_search | Numerical analysis |
| title_full | Numerical analysis Lee W. Johnson ; Ronald D. Riess* |
| title_fullStr | Numerical analysis Lee W. Johnson ; Ronald D. Riess* |
| title_full_unstemmed | Numerical analysis Lee W. Johnson ; Ronald D. Riess* |
| title_short | Numerical analysis |
| title_sort | numerical analysis |
| topic | Analyse numérique EDP inriac analyse numérique inriac approximation inriac dérivation numérique inriac interpolation inriac intégration numérique inriac optimisation inriac problème valeur propre inriac système équation linéaire inriac équation différentielle ordinaire inriac équation non linéaire inriac Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique EDP analyse numérique approximation dérivation numérique interpolation intégration numérique optimisation problème valeur propre système équation linéaire équation différentielle ordinaire équation non linéaire Numerical analysis Numerische Mathematik Einführung |
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