- 数值分析(英文版)
- - 作者：编者:凌智//蒋涛//黄健飞//张来
  - 出版社：科学
  - ISBN：9787030792785
  - 出版日期：2025/01/01
  - 页数：242
- 售价：39.2

内容大纲
数值分析随计算机的发展和使用逐渐受到科学计算工作者的广泛重视，是一种如何利用计算机解决数学问题的近似方法。随科技发展和各种行业迅速崛起的需要，高效的计算方法与高性能并行计算机硬件的需要同等受到当前科学研究的重视。科学计算己与实验、理论分析共同成为现在科学研究的三大重要手段。数值计算的核心是给出和研究各种数学问题的高效而稳定的算法，包括算法的收敛和稳定性讨论。本书主要为高校理工科研究生专业开设的“数值分析或计算方法”课程编写的教材，重点介绍常用数值计算方法及相关概念和理论。
作者介绍
目录
Preface
Chapter 1  Mathematical Review and Error Analysis
  1.1  Mathematical Review
  1.2  Errors and Significant Digits
    1.2.1  Truncation Error and Round-off Error
    1.2.2  Absolute Error and Relative Error
    1.2.3  Significant Digits
  1.3  Avoid the Loss of Accuracy
    1.3.1  Avoid the Subtraction of Nearly Equal Numbers.
    1.3.2  Avoid Big Numbers “Swallowing” Small Numbers
    1.3.3  Reduce Computations
    1.3.4  Avoid Dividing by a Number with Small Absolute Value
    1.3.5  Use Stable Algorithms
  1.4  Exercises
Chapter 2  Solutions of Equations in One Variable
  2.1  The Bisection Method
  2.2  Fixed-Point Iteration
    2.2.1  Basic Concepts
    2.2.2  Convergence and Error Estimation
    2.2.3  Local Convergence and Order of Convergence
  2.3  Newton’s Method and Secant Method
    2.3.1  Newton’s Method
    2.3.2  Secant Method
    2.3.3  Newton’s Method for Finding Multiple Roots
  2.4  Acceleration Techniques
  2.5  Programs
  2.6  Exercises
Chapter 3  Interpolation
  3.1  Lagrange Interpolation
  3.2  Newton Interpolation
  3.3  Aitken’s Method
  3.4  Hermite Interpolation
  3.5  Piecewise Polynomial Interpolation
  3.6  Cubic Spline Interpolation
  3.7  Programs
  3.8  Exercises.
Chapter 4  Curve Fitting and Orthogonal Polynomials
  4.1  Least Square Method
  4.2  Least Square Approximation
  4.3  Orthogonal Polynomials.
  4.4  Programs
    4.4.1  Least Square Method
    4.4.2  Least Square Approximation
  4.5  Exercises
Chapter 5  Direct Methods for Linear Systems
  5.1  Gaussian Elimination Method
    5.1.1  Linear Systems of Equation
    5.1.2  Gaussian Elimination with Backward-Substitution
  5.2  Gaussian Elimination with Partial Pivoting
  5.3  Matrix Factorization

  5.4  Two Special Types of Matrices
  5.5  Gaussian Elimination on Tridiagonal Linear Systems
  5.6  Norms of Vectors and Matrices
    5.6.1  Norms of Vectors
    5.6.2  Norms of Matrices
  5.7  Ill-Conditioned Linear System and Condition Number
  5.8  Programs
  5.9  Exercises
Chapter 6  Iterative Methods for Linear Systems
  6.1  Iterative Methods
    6.1.1  Jacobi Iterative Method.
    6.1.2  Gauss-Seidel Iterative Method
    6.1.3  SOR Method.
  6.2  Convergence Analysis for Iterative Methods
  6.3  Programs
  6.4  Exercises
Chapter 7  Numerical Differentiation and Integration
  7.1  Numerical Differentiation
    7.1.1  Three-Point Formulas and Five-Point Formulas
    7.1.2  The Method by Using Cubic Spline Interpolating Function
    7.1.3  Varying Step Size Midpoint Method
    7.1.4  Richardson Extrapolation
  7.2  Elements of Numerical Integration
  7.3  Newton-Cotes Quadrature Formulas.
    7.3.1  Basic Concepts of Newton-Cotes Quadrature Formulas
    7.3.2  Some Common Newton-Cotes Formulas
  7.4  Composite Numerical Integration
  7.5  Romberg Integration
    7.5.1  Recursive Trapezoidal Rule
    7.5.2  Romberg Integration
  7.6  Gaussian Quadrature
    7.6.1  Basic Concepts
    7.6.2  Two Common Gaussian Quadrature Formulas
    7.6.3  Stability and Convergence
  7.7  Programs
  7.8  Exercises
Chapter 8  Numerical Solutions of Ordinary Differential Equations
  8.1  Elements of Initial Problems
  8.2  Euler Method and Modified Euler Method
    8.2.1  Euler Method and Trapezoidal Method.
    8.2.2  Modified Euler Method
    8.2.3  Local Truncation Error
  8.3  Runge-Kutta Methods
    8.3.1  Second-Order Runge-Kutta Methods
    8.3.2  Some Common Third-and Fourth-Order Runge-Kutta Methods
  8.4  Stability and Convergence
  8.5  Multistep Methods
  8.6  Programs
  8.7  Exercises
Chapter 9  Approximating Eigenvalues and Eigenvectors

  9.1  Fundamental Theorems
  9.2  The Power Method
  9.3  Accelerating Convergence
  9.4  Inverse Power Method
  9.5  Householder’s Method
  9.6  The QR method
  9.7  Programs
  9.8  Exercises
References
Appendix A  English-Chinese Math Key Words
Appendix B  Some Math Expressions and Pronunciations

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