Description

Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board.

Key Features

  • Over 500 numerical algorithms, their fundamental principles, and applications
  • Graphs are used extensively to clarify the complexity of problems
  • Includes coded genetic algorithms
  • Includes the Lagrange multiplier method
  • User-friendly and written in a conversational style

Readership

Professionals in engineering, bioengineering, and computer science fields and scientists needing user-friendly text to solve specific problems in numerical analysis; Research Professors and students in universities

Table of Contents

Dedication

Preface

List of Figures

An Introduction to Matlab®

1.1 The MATLAB Software Package

1.2 Matrices and Matrix Operations in MATLAB

1.3 Manipulating the Elements of a Matrix

1.4 Transposing Matrices

1.5 Special Matrices

1.6 Generating Matrices and Vectors with Specified Element Values

1.7 Matrix Functions

1.8 Using the MATLAB\ Operator for Matrix Division

1.9 Element-by-Element Operations

1.10 Scalar Operations and Functions

1.11 String Variables

1.12 Input and Output in MATLAB

1.13 MATLAB Graphics

1.14 Three-Dimensional Graphics

1.15 Manipulating Graphics—Handle Graphics

1.16 Scripting in MATLAB

1.17 User-Defined Functions in MATLAB

1.18 Data Structures in MATLAB

1.19 Editing MATLAB Scripts

1.20 Some Pitfalls in MATLAB

1.21 Faster Calculations in MATLAB

2. Linear Equations and Eigensystems

2.1 Introduction

2.2 Linear Equation Systems

2.3 Operators \ and / for Solving Ax = b

2.4 Accuracy of Solutions and Ill-Conditioning

2.5 Elementary Row Operations

2.6 Solution of Ax = b by Gaussian Elimination

2.7 LU Decomposition

2.8 Cholesky Decomposition

2.9 QR Decomposition

2.10 Singular Value Decomposition

2.11 The Pseudo-Inverse

2.12 Over- and Underdetermined Systems

2.13 Iterative Methods

2.14 Sparse Matrices

2.15 The Eigenvalue Problem

2.16 Iterative Methods for Solving the Eigenvalue Problem

2.17 The MATLAB Function eig

2.18 Summary

3. Solution of Nonlinear Equations

3.1 Introduction

3.2 The Nature of Solutions to Nonlinear Equations

3.3 The Bisection Algorithm

3.4 Iterative or Fixed Point Methods

3.5 The Convergence of Iterative Methods

3.6 Ranges for C

Details

No. of pages:
552
Language:
English
Copyright:
© 2012
Published:
Imprint:
Academic Press
eBook ISBN:
9780123869883
Print ISBN:
9780123869425

About the authors

George Lindfield

Affiliations and Expertise

Professor, School of Engineering and Applied Science Aston University

John Penny

Affiliations and Expertise

Professor, School of Engineering and Applied Science Aston University