Applied Numerical Analysis Using MATLAB, 2/e (IE-Paperback)
暫譯: 使用 MATLAB 的應用數值分析（第二版）
Laurene v. Fausett
- 出版商: Prentice Hall
- 出版日期: 2007-04-10
- 定價: $1,150
- 售價: 9.8 折 $1,127
- 語言: 英文
- 頁數: 688
- ISBN: 0132068729
- ISBN-13: 9780132068727
-
相關分類:
Matlab、數值分析 Numerical-analysis
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商品描述
Description
This text is appropriate for undergraduate courses on numerical methods and numerical analysis found in engineering, mathematics & computer science departments.
Each chapter uses introductory problems from specific applications. These easy-to-understand problems clarify for the reader the need for a particular mathematical technique. Numerical techniques are explained with an emphasis on why they work.
Table of Contents
Preface
1 Foundations 1
1.1 Introductory Examples
1.1.1 Nonlinear Equations
1.1.2 Linear Systems
1.1.3 Numerical Integration
1.2 Useful Background
1.2.1 Results from Calculus
1.2.2 Results from Linear Algebra
1.2.3 A Little Information
1.3.1 Error
1.3.2 Convergence
1.3.3 Getting Better Results
1.4 Using MATLAB
1.4.1 Command Window Computations
1.4.2 M-Files
1.4.3 Programming in MATLAB
1.4.4 Matrix Multiplication
1.5 Chapter Wrap-Up
2 Functions of One Variable 47
2.1 Bisection Method
2.2 Secant-Type Methods
2.2.1 Regula Falsi
2.2.2 Secant Method
2.2.3 Analysis
2.3 Newton’s Method
2.4 Muller’s Method
2.5 Minimization
2.5.1 Golden-Section Search
2.5.2 Brent’s Method
2.6 Beyond the Basics
2.6.1 Using MATLAB’s Functions
2.6.2 Laguerre’s Method
2.6.3 Zeros of a Nonlinear Function
2.7 Chapter Wrap-Up
3 Solving Linear Systems: Direct Methods 95
3.1 Gaussian Elimination
3.1.1 Basic Method
3.1.2 Row Pivoting .
3.2 Gauss-Jordan
3.2.1 Inverse of a Matrix
3.3 Tridiagonal Systems
3.4 Further Topics
3.4.1 MATLAB’s Methods
3.4.2 Condition of a Matrix
3.4.3 Iterative Refinement
3.5 Chapter Wrap-Up
4 LU and QR Factorization 135
4.1 LU Factorization
4.1.1 Using Gaussian Elimination
4.1.2 Direct LU Factorization
4.1.3 Applications
4.2 Matrix Transformations
4.2.1 Householder Transformation
4.2.2 Givens Rotations
4.3 QR Factorization
4.3.1 Using Householder Transformations
4.3.2 Using Givens Rotations
4.4 Beyond the Basics
4.4.1 LU Factorization with Implicit Row Pivoting
4.4.2 Efficient Conversion to Hessenberg Form
4.4.3 Using MATLAB’s Functions
4.5 Chapter Wrap-Up
5 Eigenvalues and Eigenvectors 179
5.1 Power Method
5.1.1 Basic Power Method
5.1.2 Rayleigh Quotient
5.1.3 Shifted Power Method
5.1.4 Accelerating Convergence
5.2 Inverse Power Method
5.2.1 General Inverse Power Method
5.2.2 Convergence
5.3 QR Method
5.3.1 Basic QR Method
5.3.2 Better QR Method
5.3.3 Finding Eigenvectors
5.3.4 Accelerating Convergence
5.4 Further Topics
5.4.1 Singular Value Decomposition
5.4.2 MATLAB’s Methods
5.5 Chapter Wrap-Up
6 Solving Linear Systems: Iterative Methods 213
6.1 Jacobi Method
6.2 Gauss-Seidel Method
6.3 Successive Over-Relaxation
6.4 Beyond the Basics
6.4.1 MATLAB’s Built-In Functions
6.4.2 Conjugate Gradient Methods
6.4.3 GMRES
6.4.4 Simplex Method
6.5 Chapter Wrap-Up
7 Nonlinear Functions of Several Variables 251
7.1 Nonlinear Systems
7.1.1 Newton’s Method
7.1.2 Secant Methods
7.1.3 Fixed-Point Iteration
7.2 Minimization
7.2.1 Descent Methods
7.2.2 Quasi-Newton Methods
7.3 Further Topics
7.3.1 Levenberg-Marquardt Method
7.3.2 Nelder-Mead Simplex Search
7.4 Chapter Wrap-Up
8 Interpolation 275
8.1 Polynomial Interpolation
8.1.1 Lagrange Form
8.1.2 Newton Form
8.1.3 Difficulties
8.2 Hermite Interpolation
8.3 Piecewise Polynomial Interpolation
8.3.1 Piecewise Linear Interpolation
8.3.2 Piecewise Quadratic Interpolation
8.3.3 Piecewise Cubic Hermite Interpolation
8.3.4 Cubic Spline Interpolation
8.4 Beyond the Basics
8.4.1 Rational-Function Interpolation
8.4.2 Using MATLAB’s Functions
8.5 Chapter Wrap-Up
9 Approximation 333
9.1 Least-Squares Approximation
9.1.1 Approximation by a Straight Line
9.1.2 Approximation by a Parabola
9.1.3 General Least-Squares Approximation
9.1.4 Approximation for Other Functional Forms
9.2 Continuous Least-Squares Approximation
9.2.1 Approximation Using Powers of x
9.2.2 Orthogonal Polynomials
9.2.3 Legendre Polynomials
9.2.4 Chebyshev Polynomials
9.3 Function Approximation at a Point
9.3.1 Pad´e Approximation
9.3.2 Taylor Approximation
9.4 Further Topics
9.4.1 Bezier Curves
9.4.2 Using MATLAB’s Functions
9.5 Chapter Wrap-Up
10 Fourier Methods 373
10.1 Fourier Approximation and Interpolation
10.1.1 Derivation
10.1.2 Data on Other Intervals
10.2 Radix-2 Fourier Transforms
10.2.1 Discrete Fourier Transform
10.2.2 Fast Fourier Transform
10.2.3 Matrix Form of FFT
10.2.4 Algebraic Form of FFT
10.3 Mixed-Radix FFT
10.4 Using MATLAB’s Functions
10.5 Chapter Wrap-Up
11 Numerical Differentiation and Integration 405
11.1 Differentiation
11.1.1 First Derivatives
11.1.2 Higher Derivatives
11.1.3 Partial Derivatives
11.1.4 Richardson Extrapolation
11.2 Numerical Integration
11.2.1 Trapezoid Rule
11.2.2 Simpson’s Rule
11.2.3 Newton-Cotes Open Formulas
11.2.4 Extrapolation Methods
11.3 Quadrature
11.3.1 Gaussian Quadrature
11.3.2 Other Gauss-Type Quadratures
11.4 MATLAB’s Methods
11.4.1 Differentiation
11.4.2 Integration
11.5 Chapter Wrap-Up
12 Ordinary Differential Equations: Fundamentals 445
12.1 Euler’s Method
12.1.1 Geometric Introduction
12.1.2 Approximating the Derivative
12.1.3 Approximating the Integral
12.1.4 Using Taylor Series
12.2 Runge-Kutta Methods
12.2.1 Second-Order Runge-Kutta Methods
12.2.2 Third-Order Runge-Kutta Methods
12.2.3 Classic Runge-Kutta Method
12.2.4 Fourth-Order Runge-Kutta Methods
12.2.5 Fifth-Order Runge-Kutta Methods
12.2.6 Runge-Kutta-Fehlberg Methods
12.3 Multistep Methods
12.3.1 Adams-Bashforth Methods
12.3.2 Adams-Moulton Methods
12.3.3 Adams Predictor-Corrector Methods
12.3.4 Other Predictor-Corrector Methods
12.4 Further Topics
12.4.1 MATLAB’s Methods
12.4.2 Consistency and Convergence
12.5 Chapter Wrap-Up
13 ODE: Systems, Stiffness, Stability 499
13.1 Systems
13.1.1 Systems of Two ODE
13.1.2 Euler’s Method for Systems
13.1.3 Runge-Kutta Methods for Systems
13.1.4 Multistep Methods for Systems
13.1.5 Second-Order ODE
13.2 Stiff ODE
13.2.1 BDF Methods
13.2.2 Implicit Runge-Kutta Methods
13.3 Stability
13.3.1 A-Stable and Stiffly Stable Methods
13.3.2 Stability in the Limit
13.4 Further Topics
13.4.1 MATLAB’s Methods for Stiff ODE
13.4.2 Extrapolation Methods
13.4.3 Rosenbrock Methods
13.4.4 Multivalue Methods
13.5 Chapter Wrap-Up
14 ODE: Boundary-Value Problems 561
14.1 Shooting Method
14.1.1 Linear ODE
14.1.2 Nonlinear ODE
14.2 Finite-Difference Method
14.2.1 Linear ODE
14.2.2 Nonlinear ODE
14.3 Function Space Methods
14.3.1 Collocation
14.3.2 Rayleigh-Ritz
14.4 Chapter Wrap-Up
15 Partial Differential Equations 593
15.1 Heat Equation: Parabolic PDE
15.1.1 Explicit Method
15.1.2 Implicit Method
15.1.3 Crank-Nicolson Method
15.1.4 Insulated Boundary
15.2 Wave Equation: Hyperbolic PDE
15.2.1 Explicit Method
15.2.2 Implicit Method
15.3 Poisson Equation: Elliptic PDE
15.4 Finite-Element Method for Elliptic PDE
15.4.1 Defining the Subregions
15.4.2 Defining the Basis Functions
15.4.3 Computing the Coefficients
15.4.4 Using MATLAB
15.5 Chapter Wrap-Up
Bibliography 643
Answers 653
Index 667
商品描述(中文翻譯)
描述
這本書適合用於工程、數學及計算機科學系的本科數值方法和數值分析課程。
每一章都使用特定應用的入門問題。這些易於理解的問題幫助讀者明白特定數學技術的必要性。數值技術的解釋強調了它們為何有效。
目錄
前言
1 基礎 1
1.1 入門範例
1.1.1 非線性方程
1.1.2 線性系統
1.1.3 數值積分
1.2 有用的背景
1.2.1 微積分的結果
1.2.2 線性代數的結果
1.2.3 一些資訊
1.3.1 誤差
1.3.2 收斂
1.3.3 獲得更好的結果
1.4 使用 MATLAB
1.4.1 命令窗口計算
1.4.2 M-Files
1.4.3 在 MATLAB 中編程
1.4.4 矩陣乘法
1.5 章節總結
2 一變數函數 47
2.1 二分法
2.2 割線法
2.2.1 假根法
2.2.2 割線法
2.2.3 分析
2.3 牛頓法
2.4 穆勒法
2.5 最小化
2.5.1 黃金分割搜尋
2.5.2 布倫特法
2.6 超越基礎
2.6.1 使用 MATLAB 的函數
2.6.2 拉格朗日法
2.6.3 非線性函數的零點
2.7 章節總結
3 解線性系統：直接方法 95
3.1 高斯消去法
3.1.1 基本方法
3.1.2 行樞軸
3.2 高斯-喬丹法
3.2.1 矩陣的逆
3.3 三對角系統
3.4 進一步主題
3.4.1 MATLAB 的方法
3.4.2 矩陣的條件
3.4.3 迭代精煉
3.5 章節總結
4 LU 和 QR 分解 135
4.1 LU 分解
4.1.1 使用高斯消去法
4.1.2 直接 LU 分解
4.1.3 應用
4.2 矩陣變換
4.2.1 豪斯霍爾德變換
4.2.2 吉文斯旋轉
4.3 QR 分解
4.3.1 使用豪斯霍爾德變換
4.3.2 使用吉文斯旋轉
4.4 超越基礎
4.4.1 隱式行樞軸的 LU 分解
4.4.2 高效轉換為赫斯特堡形式
4.4.3 使用 MATLAB 的函數
4.5 章節總結
5 特徵值和特徵向量 179
5.1 幂法
5.1.1 基本幂法
5.1.2 雷利商
5.1.3 移位幂法
5.1.4 加速收斂
5.2 逆幂法
5.2.1 一般逆幂法
5.2.2 收斂
5.3 QR 方法
5.3.1 基本 QR 方法
5.3.2 更好的 QR 方法
5.3.3 尋找特徵向量
5.3.4 加速收斂
5.4 進一步主題
5.4.1 奇異值分解
5.4.2 MATLAB 的方法
5.5 章節總結
6 解線性系統：迭代方法 213
6.1 雅可比法
6.2 高斯-賽德法
6.3 逐次過度放鬆
