__Numerical Methods with MATLAB__ provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied.
Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical.
__Numerical Methods with MATLAB__ presents each topic in a concise and readable format to help you learn fast and effectively. It is not intended to be a reference work to the conceptual theory that underpins the numerical methods themselves. A wide range of reference works are readily available to supply this information. If, however, you want assistance in applying numerical methods then this is the book for you.

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Gupta, Abhishek

Apress, Incorporated

MATLAB solutions series, MATLAB solutions series, New York, New York State, 2014

EBL-Schweitzer, Online-ausg, Berkeley, CA, 2015

MATLAB solutions series, Berkeley, CA, 2014

United States, United States of America

Springer Nature, [Berkeley, CA], 2014

1st ed., 2014

1st ed., 2015

lg1527340

producers:
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{"edition":"1","isbns":["148420154X","1484201558","9781484201541","9781484201558"],"last_page":137,"publisher":"Apress","series":"MATLAB solutions series"}

"Learn how to apply a wide range of common numerical methods within the MATLAB environment"--Cover.
Includes index.

Contents at a Glance 3
Contents 140
About the Author 146
Acknowledgments 147
Introduction 4
Chapter 1: Introduction to MATLAB 6
Introduction 6
Interface 7
Command Window 7
Current Directory 7
Workspace 8
Figures 8
Command History 8
Editor 8
Help Browser 8
Getting Started 8
Creating a Matrix 9
Functions 10
The Difference Between Functions and Scripts 12
Special Matrices 13
Other Variable Types 14
Character Variables 14
Cells 14
Logical Variables 14
Structures 14
Saving/Loading Variables 15
Plots 15
Chapter 2: Matrix Representation, Operations and Vectorization 17
Matrix Representation 17
Conventional Sense: Matrices 17
Data Sense: Arrays 18
Model Representation 19
Operations 19
Matrix Operations 19
Dot (array) Operators 20
Arithmetic Operators 21
Logical Operators 22
Relational Operators 23
Operations for Models 23
Indexing 24
Normal Indexing 24
Linear Indexing 25
Logical Indexing 26
Clipping a Signal 26
Halving a Matrix 26
Vectorization 27
Example 1. Creating C such that C(i,j)=A(i)^B(j) 27
Example 2. Calculating the Sum of Harmonics 27
Example 3. Conversion to Matrix Operations 28
Example 4. Selective Inversion 28
Tips for Performance Improvement 29
Vectorization 29
First Attempt: Two Loops 29
Second Attempt: One Loop 29
Third Attempt: No Loop 29
Preallocating Arrays 30
Fixed Type Variables 30
Chapter 3: Numerical Techniques 31
Differentiation 31
Partial Differentiation 33
Computing Higher Derivatives 34
Integration 35
Multi-dimensional Integration 36
Integration Over an Infinite Range 36
Multidimensional Integration over Non-rectangular Intervals 37
Solving Equations 38
Polynomial Functions 38
Zeros of a General Function 38
Interpolation 40
One-dimensional Interpolation 40
Nearest Neighbor Interpolation 41
Linear Interpolation 41
Cubic Spline Interpolation 41
Cubic Interpolation 41
Spline Interpolation 41
Data Fitting and Polynomial Interpolation 41
Arbitrary Interpolation 42
Chapter 4: Visualization 43
Line Plots 43
Plot Options 45
Multiple Plots 46
Annotations 46
Handles 46
2D plots 47
Quiver Plots 47
3D Plots 48
Animations 49
A Clock Animation 49
Wave Motion 50
Movies 51
Chapter 5: Introduction to Simulation 52
One Step Simulations 52
Iterative Methods 54
Simulation of Real World Processes 56
Discrete Processes 56
Random Walks 56
Animation of the walk 58
Adding Drift 58
Simulation of Continuous Time Processes 59
Example: Balls in a 2D Box 62
Animation 63
Motion in a Force Field 65
Event-based Simulations 67
Chapter 6: Monte Carlo Simulations 71
Random Sampling 71
The Third Moment of a Gaussian Random Variable 71
Moments of Random Processes 72
Sampling Realizations of the Process 72
Time Averaging 72
Time Sampling 73
Sampling from a Given Distribution 73
Inbuilt Functions 73
Uniform Distribution 73
Gaussian Distribution 73
Exponential Distribution 73
Bernoulli Distribution 74
Rejection Sampling 74
Gibbs Sampling 75
Statistical Performance 78
Computation of pi 78
Communication Channels 79
Birth-Death Processes 79
Multidimensional Integrals 80
Summary 82
Chapter 7: Optimization 83
Optimization Overview 83
The Optimization Goal 83
Design Parameters 83
Constraints 84
The Optimization Domain 84
The Optimization Problem 84
Mathematical Approach 84
Implementation 85
Extensive Search 85
The Gradient Descent Method 86
Built-in Functions in MATLAB 87
Defining an Objective Function 87
Defining Constraints 87
Linear Constraints 87
Nonlinear constraints 88
Optimization Options 88
Problem Structures 88
Output Format 88
Minimization Problems 89
Unconstrained Minimization 89
Scalar Minimization with Bounds 90
Constrained Minimization 90
Linear Programming 91
Quadratic Programming 91
Semi-infinite Minimization 92
Multi-objective Problems 92
Equation Solving 92
Linear Equations 92
Nonlinear Equations of One Variable 93
Nonlinear Equations of Several Variables 93
Summary 93
Chapter 8: Evolutionary Computations 94
The Rastrigin Function 94
Particle Swarm Optimization 95
Algorithm 95
Implementation 96
Initialization 97
Iteration Loop 97
Updates 97
Termination Conditions 98
Iteration Ends and Outputs 98
Function Definition 98
Example 98
The Genetic Algorithm 100
Representation 100
Initialization 101
Selection 101
Crossover 101
Mutation 102
New Generation 103
Store the Best Chromosome of the Generation 103
Termination Conditions 103
Iterations 103
Output 103
Function Definition 104
Example 104
The Inbuilt Function ga 105
Simulation options 106
GUI Interface 107
Summary 107
Chapter 9: Regression and Model Fitting 108
Regression 108
Linear Regression 108
Polynomial Fitting 109
Optimization 110
Nonlinear Regression 111
Polynomial Fitting 111
General nonlinear Fitting 112
The Inbuilt Function Nlinfit 112
Generalized Linear Regression 113
Time Series Analysis 114
Autocorrelation and Proposing Models 114
Regression 115
Forecasting 115
Neural Networks 116
Feedforward Networks 116
Summary 119
Chapter 10: Differential Equations and System Dynamics 120
Differential Equations 120
Ordinary Differential Equations 120
Initial Value Problems 121
A Simplistic Method 121
Inbuilt functions 122
Events 124
Boundary Value Problems 125
Partial Differential Equations 126
System Dynamics 129
Simulation of the System 130
Step Response 131
Summary 133
Index 134
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Matrix OperationsDot (array) Operators; Arithmetic Operators; Logical Operators; Relational Operators; Operations for Models; Indexing; Normal Indexing; Linear Indexing; Logical Indexing; Clipping a Signal; Halving a Matrix; Vectorization; Example 1. Creating C such that C(i, j)=A(i)^B(j); Example 2. Calculating the Sum of Harmonics; Example 3. Conversion to Matrix Operations; Example 4. Selective Inversion; Tips for Performance Improvement; Vectorization; First Attempt: Two Loops; Second Attempt: One Loop; Third Attempt: No Loop; Preallocating Arrays; Fixed Type Variables

2016-06-29