Numerical methods and analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY u.a.
McGraw-Hill
1992
|
| Schriftenreihe: | International series in pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 751 S. graph. Darst. |
| ISBN: | 0070087172 |
Internformat
MARC
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| 100 | 1 | |a Buchanan, James L. |e Verfasser |0 (DE-588)132375648 |4 aut | |
| 245 | 1 | 0 | |a Numerical methods and analysis |c James L. Buchanan ; Peter R. Turner |
| 264 | 1 | |a New York, NY u.a. |b McGraw-Hill |c 1992 | |
| 300 | |a XV, 751 S. |b graph. Darst. | ||
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| 490 | 0 | |a International series in pure and applied mathematics | |
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Datensatz im Suchindex
| _version_ | 1804123857970266112 |
|---|---|
| adam_text | CONTENTS
Preface *»«
General Introduction 1
1 Computer Arithmetic and Errors 5
1.1 Integer Representation 5
1.2 Floating Point Numbers 8
1.3 Errors: Their Sources and Measurement 16
1.4 Errors in Floating Point Arithmetic 20
1.5 Propagation of Error 28
1.6 Summation of Series 34
1.7 Taylor Series Approximations 44
Projects 48
2 Iterative Solution of Nonlinear Equations 49
2.1 Introduction and the Bisection Method 49
2.2 Fixed Point Iteration 54
2.3 Newton s Method 62
2.4 The Secant Method 69
2.5 Acceleration of Convergence 74
2.6 Newton s Method for Two Nonlinear Equations 77
2.7 Polynomial Equation Methods 85
Projects 97
3 Approximate Evaluation of Elementary Functions 98
3.1 Introduction 98
3.2 Iterative Methods 100
3.3 Design of Computer Routines 104
3.4 CORDIC Algorithms 117
Projects 131
ix
X CONTENTS
4 Polynomial Interpolation 132
4.1 Introduction 132
4.2 The Lagrange Interpolation Polynomial 133
4.3 Divided Difference Interpolation 138
4.4 Aitken s Algorithm 150
4.5 Finite Difference Formulas 154
4.6 Choice of Nodes and Nonconvergence of Polynomial
Interpolation 163
Projects 175
5 Other Interpolation Functions 176
5.1 Introduction 176
5.2 Natural Cubic Spline Interpolation 178
5.3 Tridiagonal Systems of Equations 183
5.4 Analysis of Cubic Spline Interpolation and Cubic B Splines 192
5.5 Rational Interpolation and Continued Fractions 201
5.6 Trigonometric Interpolation and Fast Fourier Transform 208
5.7 Bivariate Interpolation 217
Projects 219
6 Systems of Linear Equations 221
6.1 Introduction 221
6.2 Partial Pivoting 228
6.3 Error Analysis 233
6.4 Matrix Factorization Methods 240
6.5 Iterative Refinement 247
6.6 Iterative Techniques 251
6.7 Acceleration and Successive Overrelaxation 257
Projects 265
7 Approximation of Functions 266
7.1 Introduction: Why Approximate? 266
7.2 Uniform Approximation 273
7.3 Least Squares Approximation 283
7.4 Systems of Orthogonal Polynomials 294
7.5 Nonpolynomial Approximation 301
7.6 Discrete Least Squares Approximation 311
7.7 Curve Fitting: Moving Least Squares 321
7.8 Curve Fitting: Bernstein Polynomials, Bezier Curves 331
Projects 345
8 Optimization 346
8.1 Introduction and Classical Results 346
8.2 Single Variable Minimization 352
8.3 Multivariate Minimization: Direct Search Methods 362
8.4 Elementary Gradient Methods 371
8.5 Conjugate Directions and Conjugate Gradient Methods 377
CONTENTS Xi
8.6 Quasi Newton Methods 389
8.7 Elimination of the Line Search 398
8.8 Introduction to Constrained Minimization 408
8.9 Systems of Nonlinear Equations 415
Projects 418
9 Numerical Calculus 419
9.1 Introduction 419
9.2 Numerical Differentiation 422
9.3 Interpolator Quadrature 432
9.4 Adaptive Quadrature 449
9.5 Richardson Extrapolation and Romberg Integration 458
9.6 Gaussian Integration 471
Projects 489
10 Numerical Solution of Differential Equations 491
10.1 Introduction: Euler s Method and Examples 491
10.2 Analysis of Euler s Method 505
10.3 Runge Kutta Methods 515
10.4 Multistep Methods 531
10.5 Variable Step Methods 549
10.6 Variable Order Methods 565
10.7 Stability and Stiff Differential Equations 576
11 The Eigenvalue Problem 597
11.1 Power and Inverse Power Methods 597
11.2 Eigenvalues of Symmetric Matrices 609
11.3 The QR Algorithm 624
12 Boundary Value Problems for Differential Equations 640
12.1 Introduction: Shooting Method 640
12.2 Finite Difference Method 652
13 The Impact of Parallel Computers 659
13.1 Introduction: Parallel Architectures 659
13.2 Basic Algorithms 668
13.3 Solution of Linear Equations: Array Processors 682
13.4 Partial Differential Equations 690
13.5 Large Sparse Systems 700
Appendix A Background Theorems in Real Analysis 714
Appendix B Background in Linear Algebra 721
Appendix C Answers to Selected Exercises 729
Bibliography 743
Index 746
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:36:26Z |
| institution | BVB |
| isbn | 0070087172 |
| language | English |
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| physical | XV, 751 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | International series in pure and applied mathematics |
| spelling | Buchanan, James L. Verfasser (DE-588)132375648 aut Numerical methods and analysis James L. Buchanan ; Peter R. Turner New York, NY u.a. McGraw-Hill 1992 XV, 751 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Turner, Peter R. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006286976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchanan, James L. Turner, Peter R. Numerical methods and analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical methods and analysis |
| title_auth | Numerical methods and analysis |
| title_exact_search | Numerical methods and analysis |
| title_full | Numerical methods and analysis James L. Buchanan ; Peter R. Turner |
| title_fullStr | Numerical methods and analysis James L. Buchanan ; Peter R. Turner |
| title_full_unstemmed | Numerical methods and analysis James L. Buchanan ; Peter R. Turner |
| title_short | Numerical methods and analysis |
| title_sort | numerical methods and analysis |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006286976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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