White Elements of Matrix Modeling and Computing with MATLAB

Erscheinungsjahr 2006
ISBN: 978-1-4200-0995-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 402 Seiten

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables.

Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applications: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. These applications are developed from very simple to more complex models. To explain the processes, the book explores numerous topics in linear algebra, including complex numbers and functions, matrices, algebraic systems, curve fitting, elements of linear differential equations, transform methods, and tools of computation. For example, the author uses linearly independent vectors and subspaces to explain over- and under-determined systems, eigenvalues and eigenvectors to solve initial value problems, and discrete Fourier transforms to perform image filtering in the frequency domain. Although the primary focus is to cultivate calculation skills by hand, most chapters also include MATLAB to help with more complicated calculations.

Zielgruppe

Students of mathematics, engineering, and sciences; applied mathematicians and engineers

Autoren/Hrsg.

White, Robert E.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

List of Figures
List of Tables
Preface
Introduction

VECTORS IN THE PLANE

Floating Point and Complex Numbers
Complex Valued Functions

Vectors in R2
Dot Product and Work

Lines and Curves in R2 and C

VECTORS IN SPACE

Vectors and Dot Product

Cross and Box Products

Lines and Curves in R3

Planes in R3

Extensions to Rn

Ax = d: UNIQUE SOLUTION

Matrix Models
Matrix Products

Special Cases of Ax = d

Row Operations and Gauss Elimination
Inverse Matrices

LU Factorization

Determinants and Cramer's Rule

Ax = d: LEAST SQUARES SOLUTION
Curve Fitting to Data
Normal Equations
Multilinear Data Fitting

Parameter Identification

Ax = d: MULTIPLE SOLUTIONS
Subspaces and Solutions in R3
Row Echelon Form
Nullspaces and Equilibrium Equations

LINEAR INITIAL VALUE PROBLEMS

First Order Linear

Second Order Linear

Homogeneous and Complex Solution

Nonhomogeneous Linear Differential Equations

System Form of Linear Second Order

EIGENVALUES AND DIFFERENTITAL EQUATIONS

Solution of x' = Ax by Elimination

Real Eigenvalues and Eigenvectors

Solution of x' = Ax + f (t)

IMAGE PROCESSING IN THE SPACE DOMAIN

Matrices and Images

Contrast and Histograms
Blurring and Sharpening

IMAGE PROCESSING IN THE FREQUENCY DOMAIN

Laplace and Fourier Transforms

Properties of DFT

DFT in Rn × Rn

Frequency Filters in Rn × Rn

Appendix: Solutions to Odd Exercises
Bibliography
Index