Details
Applied Numerical Methods Using MATLAB
2. Aufl.
123,99 € |
|
Verlag: | Wiley |
Format: | EPUB |
Veröffentl.: | 16.04.2020 |
ISBN/EAN: | 9781119626824 |
Sprache: | englisch |
Anzahl Seiten: | 656 |
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Beschreibungen
<p><b>This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLAB</b><sup>®</sup> </p> <p>This accessible book makes use of MATLAB<sup>®</sup> software to teach the fundamental concepts for applying numerical methods to solve practical engineering and/or science problems. It presents programs in a complete form so that readers can run them instantly with no programming skill, allowing them to focus on understanding the mathematical manipulation process and making interpretations of the results.</p> <p><i>Applied Numerical Methods Using MATLAB<sup>®</sup>, Second Edition</i> begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The system of linear equations is covered next, followed by a chapter on the interpolation by Lagrange polynomial. The next sections look at interpolation and curve fitting, nonlinear equations, numerical differentiation/integration, ordinary differential equations, and optimization. Numerous methods such as the Simpson, Euler, Heun, Runge-kutta, Golden Search, Nelder-Mead, and more are all covered in those chapters. The eighth chapter provides readers with matrices and Eigenvalues and Eigenvectors. The book finishes with a complete overview of differential equations.</p> <ul> <li>Provides examples and problems of solving electronic circuits and neural networks</li> <li>Includes new sections on adaptive filters, recursive least-squares estimation, Bairstow's method for a polynomial equation, and more</li> <li>Explains Mixed Integer Linear Programing (MILP) and DOA (Direction of Arrival) estimation with eigenvectors</li> <li>Aimed at students who do not like and/or do not have time to derive and prove mathematical results</li> </ul> <p><i>Applied Numerical Methods Using MATLAB<sup>®</sup>, Second Edition</i> is an excellent text for students who wish to develop their problem-solving capability without being involved in details about the MATLAB codes. It will also be useful to those who want to delve deeper into understanding underlying algorithms and equations.</p>
<p>Preface xv</p> <p>Acknowledgments xvii</p> <p>About the Companion Website xix</p> <p><b>1 MATLAB Usage and Computational Errors 1</b></p> <p>1.1 Basic Operations of MATLAB 2</p> <p>1.1.1 Input/Output of Data from MATLAB Command Window 3</p> <p>1.1.2 Input/Output of Data Through Files 3</p> <p>1.1.3 Input/Output of Data Using Keyboard 5</p> <p>1.1.4 Two-Dimensional (2D) Graphic Input/Output 6</p> <p>1.1.5 Three Dimensional (3D) Graphic Output 12</p> <p>1.1.6 Mathematical Functions 13</p> <p>1.1.7 Operations on Vectors and Matrices 16</p> <p>1.1.8 Random Number Generators 25</p> <p>1.1.9 Flow Control 27</p> <p>1.2 Computer Errors vs. Human Mistakes 31</p> <p>1.2.1 IEEE 64-bit Floating-Point Number Representation 31</p> <p>1.2.2 Various Kinds of Computing Errors 35</p> <p>1.2.3 Absolute/Relative Computing Errors 37</p> <p>1.2.4 Error Propagation 38</p> <p>1.2.5 Tips for Avoiding Large Errors 39</p> <p>1.3 Toward Good Program 42</p> <p>1.3.1 Nested Computing for Computational Efficiency 42</p> <p>1.3.2 Vector Operation vs. Loop Iteration 43</p> <p>1.3.3 Iterative Routine vs. Recursive Routine 45</p> <p>1.3.4 To Avoid Runtime Error 45</p> <p>1.3.5 Parameter Sharing via GLOBAL Variables 49</p> <p>1.3.6 Parameter Passing Through VARARGIN 50</p> <p>1.3.7 Adaptive Input Argument List 51</p> <p>Problems 52</p> <p><b>2 System of Linear Equations 77</b></p> <p>2.1 Solution for a System of Linear Equations 78</p> <p>2.1.1 The Nonsingular Case (<i>M </i>= <i>N</i>) 78</p> <p>2.1.2 The Underdetermined Case (<i>M < N</i>): Minimum-norm Solution 79</p> <p>2.1.3 The Overdetermined Case (<i>M > N</i>): Least-squares Error Solution 82</p> <p>2.1.4 Recursive Least-Squares Estimation (RLSE) 83</p> <p>2.2 Solving a System of Linear Equations 86</p> <p>2.2.1 Gauss(ian) Elimination 86</p> <p>2.2.2 Partial Pivoting 88</p> <p>2.2.3 Gauss-Jordan Elimination 97</p> <p>2.3 Inverse Matrix 100</p> <p>2.4 Decomposition (Factorization) 100</p> <p>2.4.1 <i>LU </i>Decomposition (Factorization) – Triangularization 100</p> <p>2.4.2 Other Decomposition (Factorization) – Cholesky, <i>QR </i>and SVD 105</p> <p>2.5 Iterative Methods to Solve Equations 108</p> <p>2.5.1 Jacobi Iteration 108</p> <p>2.5.2 Gauss-Seidel Iteration 111</p> <p>2.5.3 The Convergence of Jacobi and Gauss-Seidel Iterations 115</p> <p>Problems 117</p> <p><b>3 Interpolation and Curve Fitting 129</b></p> <p>3.1 Interpolation by Lagrange Polynomial 130</p> <p>3.2 Interpolation by Newton Polynomial 132</p> <p>3.3 Approximation by Chebyshev Polynomial 137</p> <p>3.4 Pade Approximation by Rational Function 142</p> <p>3.5 Interpolation by Cubic Spline 146</p> <p>3.6 Hermite Interpolating Polynomial 153</p> <p>3.7 Two-Dimensional Interpolation 155</p> <p>3.8 Curve Fitting 158</p> <p>3.8.1 Straight-Line Fit – A Polynomial Function of Degree 1 158</p> <p>3.8.2 Polynomial Curve Fit – A Polynomial Function of Higher Degree 160</p> <p>3.8.3 Exponential Curve Fit and Other Functions 165</p> <p>3.9 Fourier Transform 166</p> <p>3.9.1 FFT vs. DFT 167</p> <p>3.9.2 Physical Meaning of DFT 169</p> <p>3.9.3 Interpolation by Using DFS 172</p> <p>Problems 175</p> <p><b>4 Nonlinear Equations 197</b></p> <p>4.1 Iterative Method toward Fixed Point 197</p> <p>4.2 Bisection Method 201</p> <p>4.3 False Position or Regula Falsi Method 203</p> <p>4.4 Newton(-Raphson) Method 205</p> <p>4.5 Secant Method 208</p> <p>4.6 Newton Method for a System of Nonlinear Equations 209</p> <p>4.7 Bairstow’s Method for a Polynomial Equation 212</p> <p>4.8 Symbolic Solution for Equations 215</p> <p>4.9 Real-World Problems 216</p> <p>Problems 223</p> <p><b>5 Numerical Differentiation/Integration 245</b></p> <p>5.1 Difference Approximation for the First Derivative 246</p> <p>5.2 Approximation Error of the First Derivative 248</p> <p>5.3 Difference Approximation for Second and Higher Derivative 253</p> <p>5.4 Interpolating Polynomial and Numerical Differential 258</p> <p>5.5 Numerical Integration and Quadrature 259</p> <p>5.6 Trapezoidal Method and Simpson Method 263</p> <p>5.7 Recursive Rule and Romberg Integration 265</p> <p>5.8 Adaptive Quadrature 268</p> <p>5.9 Gauss Quadrature 272</p> <p>5.9.1 Gauss-Legendre Integration 272</p> <p>5.9.2 Gauss-Hermite Integration 275</p> <p>5.9.3 Gauss-Laguerre Integration 277</p> <p>5.9.4 Gauss-Chebyshev Integration 277</p> <p>5.10 Double Integral 278</p> <p>5.11 Integration Involving PWL Function 281</p> <p>Problems 285</p> <p><b>6 Ordinary Differential Equations 305</b></p> <p>6.1 Euler’s Method 306</p> <p>6.2 Heun’s Method – Trapezoidal Method 309</p> <p>6.3 Runge-Kutta Method 310</p> <p>6.4 Predictor-Corrector Method 312</p> <p>6.4.1 Adams-Bashforth-Moulton Method 312</p> <p>6.4.2 Hamming Method 316</p> <p>6.4.3 Comparison of Methods 317</p> <p>6.5 Vector Differential Equations 320</p> <p>6.5.1 State Equation 320</p> <p>6.5.2 Discretization of LTI State Equation 324</p> <p>6.5.3 High-order Differential Equation to State Equation 327</p> <p>6.5.4 Stiff Equation 328</p> <p>6.6 Boundary Value Problem (BVP) 333</p> <p>6.6.1 Shooting Method 333</p> <p>6.6.2 Finite Difference Method 336</p> <p>Problems 341</p> <p><b>7 Optimization 375</b></p> <p>7.1 Unconstrained Optimization 376</p> <p>7.1.1 Golden Search Method 376</p> <p>7.1.2 Quadratic Approximation Method 378</p> <p>7.1.3 Nelder-Mead Method 380</p> <p>7.1.4 Steepest Descent Method 383</p> <p>7.1.5 Newton Method 385</p> <p>7.1.6 Conjugate Gradient Method 387</p> <p>7.1.7 Simulated Annealing 389</p> <p>7.1.8 Genetic Algorithm 393</p> <p>7.2 Constrained Optimization 399</p> <p>7.2.1 Lagrange Multiplier Method 399</p> <p>7.2.2 Penalty Function Method 406</p> <p>7.3 MATLAB Built-In Functions for Optimization 409</p> <p>7.3.1 Unconstrained Optimization 409</p> <p>7.3.2 Constrained Optimization 413</p> <p>7.3.3 Linear Programming (LP) 416</p> <p>7.3.4 Mixed Integer Linear Programming (MILP) 423</p> <p>7.4 Neural Network[K-1] 433</p> <p>7.5 Adaptive Filter[Y-3] 439</p> <p>7.6 Recursive Least Square Estimation (RLSE)[Y-3] 443</p> <p>Problems 448</p> <p><b>8 Matrices and Eigenvalues 467</b></p> <p>8.1 Eigenvalues and Eigenvectors 468</p> <p>8.2 Similarity Transformation and Diagonalization 469</p> <p>8.3 Power Method 475</p> <p>8.3.1 Scaled Power Method 475</p> <p>8.3.2 Inverse Power Method 476</p> <p>8.3.3 Shifted Inverse Power Method 477</p> <p>8.4 Jacobi Method 478</p> <p>8.5 Gram-Schmidt Orthonormalization and <i>QR </i>Decomposition 481</p> <p>8.6 Physical Meaning of Eigenvalues/Eigenvectors 485</p> <p>8.7 Differential Equations with Eigenvectors 489</p> <p>8.8 DoA Estimation with Eigenvectors[Y-3] 493</p> <p>Problems 499</p> <p><b>9 Partial Differential Equations 509</b></p> <p>9.1 Elliptic PDE 510</p> <p>9.2 Parabolic PDE 515</p> <p>9.2.1 The Explicit Forward Euler Method 515</p> <p>9.2.2 The Implicit Backward Euler Method 516</p> <p>9.2.3 The Crank-Nicholson Method 518</p> <p>9.2.4 Using the MATLAB function ‘pdepe()’ 520</p> <p>9.2.5 Two-Dimensional Parabolic PDEs 523</p> <p>9.3 Hyperbolic PDES 526</p> <p>9.3.1 The Explicit Central Difference Method 526</p> <p>9.3.2 Two-Dimensional Hyperbolic PDEs 529</p> <p>9.4 Finite Element Method (FEM) for Solving PDE 532</p> <p>9.5 GUI of MATLAB for Solving PDES – PDE tool 543</p> <p>9.5.1 Basic PDEs Solvable by PDEtool 543</p> <p>9.5.2 The Usage of PDEtool 545</p> <p>9.5.3 Examples of Using PDEtool to Solve PDEs 549</p> <p>Problems 559</p> <p><b>Appendix A Mean Value Theorem 575</b></p> <p><b>Appendix B Matrix Operations/Properties 577</b></p> <p>B.1 Addition and Subtraction 578</p> <p>B.2 Multiplication 578</p> <p>B.3 Determinant 578</p> <p>B.4 Eigenvalues and Eigenvectors of a Matrix 579</p> <p>B.5 Inverse Matrix 580</p> <p>B.6 Symmetric/Hermitian Matrix 580</p> <p>B.7 Orthogonal/Unitary Matrix 581</p> <p>B.8 Permutation Matrix 581</p> <p>B.9 Rank 581</p> <p>B.10 Row Space and Null Space 581</p> <p>B.11 Row Echelon Form 582</p> <p>B.12 Positive Definiteness 582</p> <p>B.13 Scalar (Dot) Product and Vector (Cross) Product 583</p> <p>B.14 Matrix Inversion Lemma 584</p> <p><b>Appendix C Differentiation W.R.T. A Vector 585</b></p> <p><b>Appendix D Laplace Transform 587</b></p> <p><b>Appendix E Fourier Transform 589</b></p> <p><b>Appendix F Useful Formulas 591</b></p> <p><b>Appendix G Symbolic Computation 595</b></p> <p>G.1 How to Declare Symbolic Variables and Handle Symbolic Expressions 595</p> <p>G.2 Calculus 597</p> <p>G.2.1 Symbolic Summation 597</p> <p>G.2.2 Limits 597</p> <p>G.2.3 Differentiation 598</p> <p>G.2.4 Integration 598</p> <p>G.2.5 Taylor Series Expansion 599</p> <p>G.3 Linear Algebra 600</p> <p>G.4 Solving Algebraic Equations 601</p> <p>G.5 Solving Differential Equations 601</p> <p><b>Appendix H Sparse Matrices 603</b></p> <p><b>Appendix I MATLAB 605</b></p> <p>References 611</p> <p>Index 613</p> <p>Index for MATLAB Functions 619</p> <p>Index for Tables 629</p>
<p><b>Won Y. Yang, PhD,</b> is a Professor in the Department of Electrical Engineering at Chung-Ang University in Seoul, Korea. <p><b>Wenwu Cao, PhD,</b> is a Professor in the Department of Materials Science and Engineering at Penn State University in University Park, Pennsylvania. <p><b>Jaekwon Kim, PhD,</b> is a Professor in the Department of Electrical Engineering at Yongsei University in Wonju, Korea. <p><b>Kyung W. Park, PhD,</b> is a Professor in the Department of Electrical Engineering at Yonsei University, Wonju, Korea. <p><b>Ho-Hyun Park, PhD,</b> is a Professor in the School of Electrical and Electronics Engineering at Chung-Ang University in Seoul, Korea. <p><b>Jingon Joung, PhD,</b> is a Professor in the Department of Electrical Engineering at Chung-Ang University in Seoul, Korea. <p><b>Jong-Suk Ro</b> is Creative Research Engineer Development at Brain Korea 21 Plus, Seoul National University in Seoul, Korea. <p><b>Han L. Lee, PhD,</b> is a Professor in the Department of Electrical Engineering at Chung-Ang University in Seoul, Korea. <p><b>Cheol-Ho Hong</b> is Assistant Professor in the School of Electrical and Electronics Engineering at Chung-Ang University in Seoul, Korea. <p><b>Taeho Im, PhD,</b> is a Professor in Oceanic IT Engineering at Hoseo University in Asan, Korea.
<p><b>This new edition provides an updated approach for students, engineers, and researchers to apply numerical methods for solving problems using MATLAB<sup>®</sup></b> <p>This accessible book makes use of MATLAB<sup>®</sup> software to teach the fundamental concepts for applying numerical methods to solve practical engineering and/or science problems. It presents programs in a complete form so that readers can run them instantly with no programming skill, allowing them to focus on understanding the mathematical manipulation process and making interpretations of the results. <p><i>Applied Numerical Methods Using MATLAB<sup>®</sup>, Second Edition</i> begins with an introduction to MATLAB usage and computational errors, covering everything from input/output of data, to various kinds of computing errors, and on to parameter sharing and passing, and more. The system of linear equations is covered next, followed by a chapter on the interpolation by Lagrange polynomial. The next sections look at interpolation and curve fitting, nonlinear equations, numerical differentiation/integration, ordinary differential equations, and optimization. Numerous methods such as the Simpson, Euler, Heun, Runge-kutta, Golden Search, Nelder-Mead, and more are all covered in those chapters. The eighth chapter provides readers with matrices and Eigenvalues and Eigenvectors. The book finishes with a complete overview of differential equations. <ul> <li>Provides examples and problems of solving electronic circuits and neural networks</li> <li>Includes new sections on adaptive filters, recursive least-squares estimation, Bairstow's method for a polynomial equation, and more</li> <li>Explains Mixed Integer Linear Programing (MILP) and DOA (Direction of Arrival) estimation with eigenvectors</li> <li>Aimed at students who do not like and/or do not have time to derive and prove mathematical results</li> </ul> <p><i>Applied Numerical Methods Using MATLAB<sup>®</sup>, Second Edition</i> is an excellent text for students who wish to develop their problem-solving capability without being involved in details about the MATLAB codes. It will also be useful to those who want to delve deeper into understanding underlying algorithms and equations.