Numerical methods using MATLAB:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Elsevier, AP, Academic Press
[2019]
|
| Edition: | Fourth edition |
| Series: | MATLAB examples
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxv, 582 Seiten Illustrationen, Diagramme |
| ISBN: | 9780128122563 |
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Record in the Search Index
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| adam_text | Contents List of Figures ..................................................................................................................................... xiii About the Authors ............................................................................................................................... xxi Preface.............................................................................................................................................. xxiii Acknowledgment................................................................................................................................... xxv CHAPTER 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 CHAPTER 2 2.1 2.2 2.3 2.4 2.5 An Introduction to Matlab® ................................................................................. The Software Package Matlab ............................................................................ Matrices in Matlab............................................................................................... Manipulating the Elements of a Matrix ................................................................ Transposing Matrices............................................................................................... Special Matrices ...................................................................................................... Generating Matrices and Vectors With Specified Element Values...................... Matrix Algebra in
Matlab.................................................................................... Matrix Functions...................................................................................................... Using the Matlab Operator for Matrix Division................................................ Element-by-Element Operations ............................................................................ Scalar Operations and Functions ............................................................................ String Variables........................................................................................................ Input and Output in MATLAB ................................................................................ Matlab Graphics.................................................................................................... Three-Dimensional Graphics.................................................................................. Implicit Graphics...................................................................................................... Manipulating Graphics - Handle Graphics............................................................ Scripting in Matlab ............................................................................................. User-Defined Functions in Matlab ..................................................................... Data Structures in Matlab.................................................................................... Editing Matlab
Scripts......................................................................................... Some Pitfalls in Matlab ....................................................................................... Speeding up Calculations in Matlab................................................................... Live Editor .............................................................................................................. Summary................................................................................................................... Problems..................................................................................... 1 1 3 5 8 9 10 13 14 15 15 17 20 25 28 35 37 39 45 51 58 62 64 65 66 66 66 Linear Equations and Eigensystems...................................................................... Introduction............................................................................................................... Linear Equation Systems................................................................................. Operators and / for Solving Ax = b..................................................................... Accuracy of Solutions and Ill-Conditioning.......................................................... Elementary Row Operations .................................................................................. 73 73 76 81 85 88 VII
viii Contents 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 Solution of Ах = b by Gaussian Elimination.......................................................... LU Decomposition .......................... ...................................................................... Cholesky Decomposition......................................................................................... QR Decomposition .................................................................................................. Singular Value Decomposition................................................................................ The Pseudo-Inverse.................................................................................................. Over-and Under-Determined Systems................................................................... Iterative Methods...................................................................................................... Sparse Matrices......................................................................................................... The Eigenvalue Problem ......................................................................................... 2.15.1 Eigenvalue Decomposition .......................................................................... 2.15.2 Comparing Eigenvalue and Singular Value Decomposition .................... Iterative Methods for Solving the Eigenvalue Problem........................................ Solution of the General Eigenvalue Problem ......................................................... The Google‘PageRank’Algorithm
....................................................................... Summary.................................................................................................................... Problems.................................................................................................................... 89 91 95 97 101 104 109 117 118 128 135 138 140 145 149 151 152 Solution of Non-Linear Equations ........................................................................ 3.1 Introduction............................................................................................................... 3.2 The Nature of Solutions to Non-Linear Equations ............................................... 3.3 The Bisection Algorithm......................................................................................... 3.4 Iterative or Fixed Point Methods ............................................................................ 3.5 The Convergence of Iterative Methods................................................................... 3.6 Ranges for Convergence and Chaotic Behavior ................................................... 3.7 Newton’s Method .................................................................................................... 3.8 Schroder’s Method.................................................................................................... 3.9 Numerical Problems ............................................................................................... 3.10 The Matlab Function fzero and Comparative
Studies...................................... 3.11 Methods for Finding all the Roots of a Polynomial............................................... 3.11.1 Bairstow’s Method ....................................................................................... 3.11.2 Laguerre’s Method ....................................................................................... 3.12 Solving Systems of Non-Linear Equations............................................................ 3.13 Broyden’s Method for Solving Non-Linear Equations ........................................ 3.14 Comparing the Newton and Broyden Methods...................................................... 3.15 Summary...................................................................................................... 3.16 Problems.................................................................................................................... 157 157 159 160 160 161 162 164 169 170 171 173 173 177 178 181 184 185 185 2.16 2.17 2.18 2.19 2.20 CHAPTER 3 , CHAPTER 4 4.1 4.2 4.3 4.4 4.5 Differentiation and Integration ........................................... 191 Introduction............................................................................................................... 191 Numerical Differentiation ....................................................................................... 191 Numerical Integration .............................................................................................. 195 Simpson’s
Rule......................................................................................................... 196 Newton-Cotes Formulae......................................................................................... 200
Contents 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 CHAPTER 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 ix Romberg Integration ............................................................................. Gaussian Integration ................................................................................................ Infinite Ranges of Integration.................................................................................. 4.8.1 Gauss-Laguerre Formula ............................................................................ 4.8.2 Gauss-Hermite Formula.............................................................................. Gauss-Chebyshev Formula .................................................................................... Gauss-Lobatto Integration......................................................... Filon’s Sine and Cosine Formulae ......................................................................... Adaptive Integration ............................................................................................... Problems in the Evaluation of Integrals ................................................................. Test Integrals............................................................................................................. Repeated Integrals.................................................................................................... 4.15.1 Simpson’s Rule for Repeated Integrals ..................................................... 4.15.2 Gaussian Integration for
RepeatedIntegrals................................................ Matlab Functions for Double and TripleIntegration ......................................... Summary.................................................................................................................... Problems.................................................................................................................... 201 203 205 205 208 210 210 214 218 223 224 225 225 227 230 231 231 Solution of Differential Equations ........................................................ 239 239 240 242 244 247 251 253 256 256 260 260 262 264 264 265 271 271 273 276 280 282 285 287 295 295 Introduction............................................................................................................... Euler’s Method ........................................................................................................ The Problem of Stability ......................................................................................... The Trapezoidal Method ......................................................................................... Runge-Kutta Methods............................................................................................. Predictor-Corrector Methods.................................................................................. Hamming’s Method and the Use of ErrorEstimates............................................. Error Propagation in Differential Equations.......................... The Stability of Particular Numerical
Methods..................................................... Systems of Simultaneous Differential Equations................................................... 5.10.1 Zeeman Model ............................................................................................. 5.10.2 The Predator-Prey Problem.......... ............................................................... 5.11 Higher-Order Differential Equations ..................................................................... 5.11.1 Conversion to a Set of Simultaneous First-Order Differential Equations . 5.11.2 Newmark’s Method....................................................................................... 5.12 Chaotic Systems ...................................................................................................... 5.12.1 The Lorenz Equations.................................................................................. 5.12.2 Duffing’s Equation ...................................................................................... 5.13 Differential Equations Applied to NeuralNetworks ............................................. 5.14 Stiff Equations........................................................................................................... 5.15 Special Techniques ................................................................................................. 5.16 Extrapolation Techniques......................................................................................... 5.17
Simulink................................................................................................................... 5.18 Summary........... ........................................................................................................ 5.19 Problems...................................................................................................................
x Contents CHAPTER 6 Boundary Value Problems........................................................................................ 6.1 Classification of Second-Order Differential Equations ........................................ 6.2 The Shooting Method .............................................................................................. 6.3 The Finite Difference Method ................................................................................ 6.4 Two-Point Boundary Value Problems..................................................................... 6.5 Parabolic Partial Differential Equations................................................................. 6.6 Hyperbolic Partial Differential Equations............................................................... 6.7 Elliptic Partial Differential Equations..................................................................... 6.8 Summary.................................................................................................................... 6.9 Problems.................................................................................................................... 301 301 302 304 306 313 316 319 326 326 CHAPTER 7 Analyzing Data.......................................................................................................... 7.1 Introduction............................................................................................................... 7.2 Interpolation Using Polynomials ............................................................................ 7.3 Interpolation Using
Splines..................................................................................... 7.4 Multiple Regression: Least Squares Criterion........................................................ 7.5 Diagnostics for Model Improvement ..................................................................... 7.6 Analysis of Residuals .............................................................................................. 7.7 Polynomial Regression ............................................................................................ 7.8 Fitting General Functions to Data............................................................................ 7.9 Non-Linear Least Squares Regression ................................................................... 7.10 Transforming Data.................................................................................................... 7.11 The Kalman Filter.................................................................................................... 7.12 Principal Component Analysis................................................................................ 7.13 Summary.................................................................................................................... 7.14 Problems.................................................................................................................... 329 329 329 333 336 339 343 348 355 356 359 362 371 377 377 CHAPTER 8 Analyzing Data Using Discrete Transforms........................................................... 383 8.1
Introduction............................................................................................................... 383 8.2 Fourier Analysis of Discrete Data .......................................................................... 383 8.3 The Hilbert Transform.............................................................................................. 398 8.4 The Walsh Transforms.............................................................................................. 407 8.5 Introduction to Wavelet Analysis............................................................................ 413 8.6 Discrete Wavelet Transforms................................................................................... 415 8.6.1 Haar Wavelet ................................................................................................ 415 8.6.2 Daubechies Wavelets..................................................................................... 423 8.7 Continuous Wavelet Transforms.............................................................................. 425 8.8 Summary.................................................................................................................... 429 8.9 Problems.................................................................................................................... 429 CHAPTER 9 Optimization Methods............................................................................................... 9.1 Introduction...............................................................................................................
9.2 Linear Programming Problems................................................................................ 9.3 Optimizing Single-Variable Functions................................................................... 9.4 The Conjugate Gradient Method ............................................................................ 433 433 433 440 443
Contents XI 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 Moller’s Scaled Conjugate Gradient Method ........................................................ Conjugate Gradient Method for Solving Linear Systems ................................... Metaheuristic Methods ........................................................................................... Simulated Annealing................................................................................................ Evolutionary Algorithm........................................................................................... Differential Evolution ............................................................................................. Constrained Non-Linear Optimization................................................................... The Sequential Unconstrained Minimization Technique...................................... Summary.................................................................................................................... Problems.................................................................................................................... 449 455 457 457 461 466 472 476 479 480 CHAPTER 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 10.14 10.15 10.16 10.17 Applications of the Symbolic Toolbox ......................................... Introduction to the Symbolic Toolbox .................................................................. Symbolic Variables and Expressions .................................................................... Variable Precision
Arithmetic in Symbolic Calculations..................................... Series Expansion and Summation ......................................................................... Manipulation of Symbolic Matrices...................................................................... Symbolic Methods for the Solution of Equations ................................................. Special Functions .................................................................................................... Symbolic Differentiation.................................................................................... Symbolic Partial Differentiation............................................................................. Symbolic Integration................................................................................................ Symbolic Solution of Ordinary Differential Equations ........................................ The Laplace Transform ........................................................................................... The Z-Transform...................................................................................................... Fourier Transform Methods.................................................................................... Linking Symbolic and Numerical Processes....................................... Summary.................................................................................................................... Problems....................................................................................................................
485 485 486 490 491 494 498 500 502 503 504 508 513 515 517 521 523 523 Appendix A A.1 A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9 A. 10 A.11 A. 12 A. 13 Matrix Algebra......................................................................................................... Introduction............................................................................................................... Matrices and Vectors............................................................................................... Some Special Matrices............................................................................................. Determinants............................................................................................................ Matrix Operations................................................................................................... Complex Matrices.................................................................................................... Matrix Properties............. ........................................................................................ Some Matrix Relationships .................................................................................... Eigenvalues............................................................................................................... Definition of Norms................................................................................................. Reduced Row Echelon Form.................................................................................. Differentiating
Matrices........................................................................................... Square Root of a Matrix........................................................................ 529 529 529 530 531 531 533 534 534 534 535 536 536 537
xii Contents Appendix В B.1 B.2 B.3 Error Analysis ..................................................................................................... 539 Introduction................................................................................................................ Errors in Arithmetic Operations............................................................................... Errors in the Solution of Linear Equation Systems................................................ 539 540 541 Solutions to Selected Problems........................................................................................................... 545 Bibliography.......................................................................................................................................... 565 Index ..................................................................................................................................................... 569
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| institution | BVB |
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| record_format | marc |
| series2 | MATLAB examples |
| spelling | Lindfield, George R. 20. Jht. Verfasser (DE-588)1089199910 aut Numerical methods using MATLAB George Lindfield (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom), John Penny (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom) Fourth edition London Elsevier, AP, Academic Press [2019] xxv, 582 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier MATLAB examples Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Visualisierung (DE-588)4188417-6 gnd rswk-swf Programm (DE-588)4047394-6 gnd rswk-swf Visualisierung (DE-588)4188417-6 s Numerische Mathematik (DE-588)4042805-9 s Programm (DE-588)4047394-6 s DE-604 MATLAB (DE-588)4329066-8 s 1\p DE-604 Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Penny, John E. T. 20. Jht. Verfasser (DE-588)1089199902 aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030630221&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lindfield, George R. 20. Jht Penny, John E. T. 20. Jht Numerical methods using MATLAB Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Visualisierung (DE-588)4188417-6 gnd Programm (DE-588)4047394-6 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042805-9 (DE-588)4329066-8 (DE-588)4188417-6 (DE-588)4047394-6 |
| title | Numerical methods using MATLAB |
| title_auth | Numerical methods using MATLAB |
| title_exact_search | Numerical methods using MATLAB |
| title_full | Numerical methods using MATLAB George Lindfield (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom), John Penny (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom) |
| title_fullStr | Numerical methods using MATLAB George Lindfield (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom), John Penny (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom) |
| title_full_unstemmed | Numerical methods using MATLAB George Lindfield (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom), John Penny (Aston University, School of Engineering and Applied Science, Birmingham, England, United Kingdom) |
| title_short | Numerical methods using MATLAB |
| title_sort | numerical methods using matlab |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Visualisierung (DE-588)4188417-6 gnd Programm (DE-588)4047394-6 gnd |
| topic_facet | Numerisches Verfahren Numerische Mathematik MATLAB Visualisierung Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030630221&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lindfieldgeorger numericalmethodsusingmatlab AT pennyjohnet numericalmethodsusingmatlab |