本书以英文版的形式介绍各种数值计算方法以及相关的基本概念和理论。内容主要包括误差问题,非线性方程的数值解,插值与多项式逼近,数值积分,解线性方程组的直接法,解大型线系统的迭代技术,矩阵的特征值和特征向量以及常微分方程初值问题的数值解法等。会书对主要基本算法的推导、构造原理、收敛性、误差估计等进行了较详细的讨论,内容取材适当,由浅入深,各章均有例题和适量的习题以及对各种方法的便于编程的算法描述。
本书可作为理工科院校相关专业“数值分析”课程双语教学或专业英语教学的教材,也可作为非数学专业研究生“数值分析”课程的教材,并可供科技工作者和工程技术人员参考使用。

1 Preliminaries
1.1 Review of Calculus
Exercise
1.2 Round-Off Errors and Computer Arithmetic
Exercise
2 The Solution of Nonlinear Equation f(x)=0
2.1 The Bisection Algorithm
Exercise
2.2 Fixed-Point Iteration
Exercise
2.3 The Newton-Raphson Method
Exercise
2.4 Error Analysis for Iterative Methods and Acceleration Techniques
Exercise
3 Interpolation and Polynomial Approximation
3.1 Interpolation and the Lagrange Polynomial
Exercise
3.2 Divided Differences
Exercise
3.3 Hermite Interpolation
Exercise
3.4 Cubic Spline Interpolation
4 Numerical Integration
4.1 Introduction to Quadrature
Exercise
4.2 Composite Trapezoidal and Simpson's Rule
Exercise
4.3 Recursive Rules and Romberg Ingegration
Exercise
5 Diresct Methods for Solving Linear Systems
5.1 Linear Systems of Equations
Exercise
5.2 Pivoting Strategies
Exercise
5.3 Matrix Factorization
Exercise
5.4 Special Types of Matrices
Exercise
6 Iterative Techniques in Matrix Algebra
6.1 Norms of Vectors and Matrices
Exercise
6.2 Eigenvalues and Eigenvectors
Exercise
6.3 Iterative Techniques for Solving Linear Systems
Exercise
6.4 Error Estimates and Iterative Refinement
Exercise
7 Approximating Eigenvalues
8 Initial-Value Problems for Ordingary Differetial Equations