Scientific computing: an introductory survey
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics, SIAM
[2018]
|
| Ausgabe: | Revised second edition, SIAM edition |
| Schriftenreihe: | Classics in applied mathematics
80 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | This SIAM edition is a republication (with minor updating) of the second edition published by McGraw-Hill in 2002. |
| Beschreibung: | xx, 567 Seiten Illustrationen, Diagramme |
| ISBN: | 9781611975574 |
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Datensatz im Suchindex
| _version_ | 1807956399643164672 |
|---|---|
| adam_text |
Contents xiii Preface to the ClassicsEdition xv Preface Notation xix 1 ScientificComputing 1.1 1.2 1.3 1.4 1.5 Introduction 1 Approximations in Scientific Computation Computer Arithmetic 16 Mathematical Software 33 Historical Notes and Further Reading 37 2 Systems of Linear Equations 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 48 104 Linear Least Squares Problems 104 Existence and Uniqueness 108 Sensitivity and Conditioning 112 Problem Transformations 116 Orthogonalization Methods 120 Singular Value Decomposition 136 Comparison of Methods 142 Software for Linear Least Squares 143 Historical Notes and Further Reading 145 4 Eigenvalue Problems 4.1 4 Linear Systems 48 Existence and Uniqueness 50 Sensitivity and Conditioning 51 Solving Linear Systems 62 Special Types of Linear Systems 83 Iterative Methods for Linear Systems 88 Software for Linear Systems 88 Historical Notes and Further Reading 91 3 Linear Least Squares 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 1 Eigenvalues and Eigenvectors 156 156
Contents 4.2 Existence and Uniqueness 159 4.3 Sensitivity and Conditioning 165 4.4 Problem Transformations 168 4.5 Computing Eigenvalues and Eigenvectors 172 4.6 Generalized Eigenvalue Problems 200 4.7 Computing the Singular Value Decomposition 201 4.8 Software for Eigenvalue Problems 201 4.9 Historical Notes and Further Reading 203 5 Nonlinear Equations 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6 Optimization 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 215 Nonlinear Equations 215 Existence and Uniqueness 216 Sensitivity and Conditioning 220 Convergence Rates and Stopping Criteria 221 Nonlinear Equations in One Dimension 223 Systems of Nonlinear Equations 236 Software for Nonlinear Equations 242 Historical Notes and Further Reading 243 255 Optimization Problems 255 Existence and Uniqueness 258 Sensitivity and Conditioning 268 Optimization in One Dimension 269 Unconstrained Optimization 275 Nonlinear Least Squares 284 Constrained Optimization 287 Software for Optimization 294 Historical Notes and Further Reading 295 7 Interpolation 308 7.1 Interpolation 308 7.2 Existence, Uniqueness, and Conditioning 311 7.3 Polynomial Interpolation 312 7.4 Piecewise Polynomial Interpolation 325 7.5 Software for Interpolation 331 7.6 Historical Notes and Further Reading 332 8 Numerical Integration and Differentiation 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Integration 338 Existence, Uniqueness, and Conditioning 340 Numerical Quadrature 341 Other Integration Problems 358 Integral Equations 361 Numerical Differentiation 364 Richardson Extrapolation 368 338
Contents 8 8 Software for Integration and Differentiation 370 8 9 Historical Notes and Further Reading 372 9 Initial Value Problems for ODEs 91 92 9,3 9.4 9.5 10 Boundary Value Problems for ODEs 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 494 Trigonometric Interpolation 494 FFT Algorithm 497 Applications of DFT 501 Wavelets 503 Software for FFT 504 Historical Notes and Further Reading 505 13 Random Numbers and Simulation 13.1 13.2 13.3 13.4 13.5 13.6 446 Partial Differential Equations 446 Time-Dependent Problems 452 Time-Independent Problems 460 Direct Methods for Sparse Linear Systems 463 Iterative Methods for Linear Systems 466 Comparison of Methods 479 Software for Partial Differential Equations 482 Historical Notes and Further Reading 484 12 Fast Fourier Transform 12.1 12.2 12.3 12.4 12.5 12.6 421 Boundary Value Problems 421 Existence, Uniqueness, and Conditioning 423 Shooting Method 426 Finite Difference Method 429 Collocation Method 431 Galerkin Method 435 Eigenvalue Problems 439 Softwrare for ODE Boundary Value Problems 440 Historical Notes and Further Reading 441 11 Partial Differential Equations 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 381 Ordinary Differential Equations 381 Existence, Uniqueness, and Conditioning 386 Numerical Solution of ODEs 389 Software for ODE Initial Value Problems 412 Historical Notes and Further Reading 413 Stochastic Simulation 510 Randomness and Random Numbers 511 Random Number Generators 512 Quasi-Random Sequences 514 Software for Generating Random Numbers 515 Historical Notes and Further Reading 515 510
Contents Bibliography 522? Index 553
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including • proper problem formulation, • selection of effective solution algorithms, and • interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include • pointers to Python software and the Chebfun package, • expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and • about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Revised Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems. |
| adam_txt |
Contents xiii Preface to the ClassicsEdition xv Preface Notation xix 1 ScientificComputing 1.1 1.2 1.3 1.4 1.5 Introduction 1 Approximations in Scientific Computation Computer Arithmetic 16 Mathematical Software 33 Historical Notes and Further Reading 37 2 Systems of Linear Equations 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 48 104 Linear Least Squares Problems 104 Existence and Uniqueness 108 Sensitivity and Conditioning 112 Problem Transformations 116 Orthogonalization Methods 120 Singular Value Decomposition 136 Comparison of Methods 142 Software for Linear Least Squares 143 Historical Notes and Further Reading 145 4 Eigenvalue Problems 4.1 4 Linear Systems 48 Existence and Uniqueness 50 Sensitivity and Conditioning 51 Solving Linear Systems 62 Special Types of Linear Systems 83 Iterative Methods for Linear Systems 88 Software for Linear Systems 88 Historical Notes and Further Reading 91 3 Linear Least Squares 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 1 Eigenvalues and Eigenvectors 156 156
Contents 4.2 Existence and Uniqueness 159 4.3 Sensitivity and Conditioning 165 4.4 Problem Transformations 168 4.5 Computing Eigenvalues and Eigenvectors 172 4.6 Generalized Eigenvalue Problems 200 4.7 Computing the Singular Value Decomposition 201 4.8 Software for Eigenvalue Problems 201 4.9 Historical Notes and Further Reading 203 5 Nonlinear Equations 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6 Optimization 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 215 Nonlinear Equations 215 Existence and Uniqueness 216 Sensitivity and Conditioning 220 Convergence Rates and Stopping Criteria 221 Nonlinear Equations in One Dimension 223 Systems of Nonlinear Equations 236 Software for Nonlinear Equations 242 Historical Notes and Further Reading 243 255 Optimization Problems 255 Existence and Uniqueness 258 Sensitivity and Conditioning 268 Optimization in One Dimension 269 Unconstrained Optimization 275 Nonlinear Least Squares 284 Constrained Optimization 287 Software for Optimization 294 Historical Notes and Further Reading 295 7 Interpolation 308 7.1 Interpolation 308 7.2 Existence, Uniqueness, and Conditioning 311 7.3 Polynomial Interpolation 312 7.4 Piecewise Polynomial Interpolation 325 7.5 Software for Interpolation 331 7.6 Historical Notes and Further Reading 332 8 Numerical Integration and Differentiation 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Integration 338 Existence, Uniqueness, and Conditioning 340 Numerical Quadrature 341 Other Integration Problems 358 Integral Equations 361 Numerical Differentiation 364 Richardson Extrapolation 368 338
Contents 8 8 Software for Integration and Differentiation 370 8 9 Historical Notes and Further Reading 372 9 Initial Value Problems for ODEs 91 92 9,3 9.4 9.5 10 Boundary Value Problems for ODEs 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 494 Trigonometric Interpolation 494 FFT Algorithm 497 Applications of DFT 501 Wavelets 503 Software for FFT 504 Historical Notes and Further Reading 505 13 Random Numbers and Simulation 13.1 13.2 13.3 13.4 13.5 13.6 446 Partial Differential Equations 446 Time-Dependent Problems 452 Time-Independent Problems 460 Direct Methods for Sparse Linear Systems 463 Iterative Methods for Linear Systems 466 Comparison of Methods 479 Software for Partial Differential Equations 482 Historical Notes and Further Reading 484 12 Fast Fourier Transform 12.1 12.2 12.3 12.4 12.5 12.6 421 Boundary Value Problems 421 Existence, Uniqueness, and Conditioning 423 Shooting Method 426 Finite Difference Method 429 Collocation Method 431 Galerkin Method 435 Eigenvalue Problems 439 Softwrare for ODE Boundary Value Problems 440 Historical Notes and Further Reading 441 11 Partial Differential Equations 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 381 Ordinary Differential Equations 381 Existence, Uniqueness, and Conditioning 386 Numerical Solution of ODEs 389 Software for ODE Initial Value Problems 412 Historical Notes and Further Reading 413 Stochastic Simulation 510 Randomness and Random Numbers 511 Random Number Generators 512 Quasi-Random Sequences 514 Software for Generating Random Numbers 515 Historical Notes and Further Reading 515 510
Contents Bibliography 522? Index 553
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including • proper problem formulation, • selection of effective solution algorithms, and • interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include • pointers to Python software and the Chebfun package, • expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and • about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Revised Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems. |
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| spelling | Heath, Michael T. Verfasser (DE-588)1183726414 aut Scientific computing an introductory survey Michael T. Heath (University of Illinois at Urbana-Champaign, Urbana, Illinois) Revised second edition, SIAM edition Philadelphia Society for Industrial and Applied Mathematics, SIAM [2018] xx, 567 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Classics in applied mathematics 80 This SIAM edition is a republication (with minor updating) of the second edition published by McGraw-Hill in 2002. Science Data processing Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Classics in applied mathematics 80 (DE-604)BV008258410 80 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034368951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034368951&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Scientific computing an introductory survey |
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| title_exact_search | Scientific computing an introductory survey |
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| title_full | Scientific computing an introductory survey Michael T. Heath (University of Illinois at Urbana-Champaign, Urbana, Illinois) |
| title_fullStr | Scientific computing an introductory survey Michael T. Heath (University of Illinois at Urbana-Champaign, Urbana, Illinois) |
| title_full_unstemmed | Scientific computing an introductory survey Michael T. Heath (University of Illinois at Urbana-Champaign, Urbana, Illinois) |
| title_short | Scientific computing |
| title_sort | scientific computing an introductory survey |
| title_sub | an introductory survey |
| topic | Science Data processing Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Science Data processing Numerical analysis Data processing Numerische Mathematik |
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