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該書為研究生的數值分析教程,包括基礎入門課程和隨后的專業課。
后者主要針對數值線性代數、微分方程的數值解，另外增添一些與復變函數論、多維量分析（尤其在優化方面）、功能分析及其方程相關的課題。作者感覺當前的一些學科分支，尤其是那些處理線性代數和偏微分方程的學科，已經成為了當前研究的主流。
縱觀上下文，書的前四章可以作為基礎入門課程，剩下的三章可作為高年級學生的教材。
Walter Gautschi（W.高奇,美國）是國際知名學者，在數學和計算機學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。
Prologue
P1 Overview
P2 Numerical Analysis Software
P3 Textbooks and Monographs
P3.1 Selected Textbooks on Numerical Analysis
P3.2 Monographs and Books on Specialized Topics
P4 Journals
1 Machine Arithmetic and Related Matters
1.1 Real Numbers，Machine Numbers，and Rounding
1.1.1 Real Numbers
1.1.2 Machine Numbers
1.1.3 Rounding
1.2 Machine Arithmetic
1.2.1 A Modelof Machine Arithmetic
1.2.2 Error Propagation in Arithmetic Operations：Cancellation Error
1.3 The Condition of a Problem
1.3.1 Condition Numbers
1.3.2 Examples
1.4 The Condition of an Algorithm
1.5 Computer Solution of a Problem；Overall Error
1.6 Noms to Chapter 1
Exercises and Machine Assignments to Chapter 1
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
2 Approximation and Interpolation
2.1 Least Squares Approximation
2.1.1 Inner Products
2.1.3 Least Squares Error；Convergence
2.1.4 Examples of Orthogonal Systems
2.2 Polynomial Interpolation
2.2.1 Lagrange Interpolation Formula：Interpolation Operator
2.2.2 Interpolation Error
2.2.3 Convergence
2.2.4 Chebyshev Polynomials and Nodes
2.2.5 Barycentric Formula
2.2.6 Newton』s Formula
2.2.7 Hermite Interpolation
2.2.8 Inverse Interpolation
2.3 Approximation and Interpolation by Spline Functions
2.3.1 Interpolation by Piecewise Linear Functions
2.3.2 A Basis for So（△）
2.3.3 Least Squares Approximation
2.3.4 Interpolationby Cubic Splines
2.3.5 Minimality Properties of Cubic Spline Interpolants
2.4 Notes to Chapter 2
Exercises and Machine Assignments to Chapter2
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
3 Numerical Differentiation and Integration
3.1 Numerical Diflferentiation
3.1.1 A General Differentiation Formula for Unequally Spaced Points
3.1.2 Examples
3.1.3 Numerical Differentiation with Perturbed Data
3.2 Numerical Integration
3.2.1 The Composite Trapezoidal and Simpson』s Rules
3.2.2 （Weighted）Newton—Cotes and Gauss Formulae
3.2.3 Properties of Gaussian Quadrature Rules
3.2.4 Some Applications of the Gauss Quadrature Rule
3.2.5 Approximation of Linear Functionals：Method of Interpolation vs.Method Of Undetermined Coefficients
3.2.6 Peano Representation of Linear Functionals
3.2.7 Extrapolation Methods
3.3 Notesto Chapter 3
Exercises and Machine Assignments to Chapter 3
Exercises
Machine Assignments
Selected Solutionsto Exercises
Selected Solutionsto Machine Assignments
4 Nonlinear Equations
4.1 Examples
4.1.1 A Transcendental Equation
4.1.2 A Two—Point Boundary Value Problem
4.1.3 A Nonlinear Integral Equation
4.1.4 s—Orthogonal Polynomials
4.2 Iteration，Convergence，and Emciency
4.3 The Methods of Bisection and Sturm Sequences
4.3.1 Bisection Method
4.3.2 Method of Sturm Sequences
4.4 Method of False Position
4.5 Secant Method
4.6 Newton』s Method
4.7 Fixed Point Iteration
4.8 Algebraic Equations
4.8.1 Newton』s Method Applied to an Algebraic Equation
4.8.2 An Accelerated Newton Method for Equations
with Real Roots
4.9 Systems of Nonlinear Equations
4.9.1 Contraction Mapping Principle
4.9.2 Newton』s Method for Systems of Equations
4.10 Notes to Chapter4
Exercises and Machine Assignments to Chapter 4
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
5 Initial Val He Problemsfor ODEs：One—Step Methods
5.1 Examples
5.2 Tvpes of Differential Equations
5.3 Existence and Uniqueness
5.4 Numerical Methods
5.5 Local Description of One—Step Methods
5.6 Examples of One—Step Methods
5.6.1 Euler』s Method
5.6.2 Method of Tayl or Expansion
5.6.3 Improved Euler Methods
5.6.4 Second—Order Two—Stage Methods
5.6.5 Runge—Kutta Methods
5.7 Global Description of One—Step Methods
5.7.1 Stability
5.7.2 Convergence
5.7.3 Asymptotics of Global Error
2.1.2 The Normal Equations
5.8 Error Monitoring and Step Control
5.81 Estimation of Global Error
5.8.2 Truncation Error Estimates
5.83 Step Control
5.9 Stiff Problems
5.9.1 A—Stability
5.9.2 Pad6 Approximation
5.9.3 Examples of A—Stable One—Step Methods
5.9.4 Regions of Absolute Stability
5.10 Notes to Chapter5
Exercises and Machine Assignments to Chapter 5
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
6 Initial Value Problems for ODEs：Multistep Methods
6.1 Local Description of Multistep Methods
6.1.1 Explicit and Implicit Methods
6.1.2 Local Accuracy
6.1.3 Polynomial Degree VS.Order
6.2 Examples of Multistep Methods
6.2.1 Adams—Bashforth Method
6.2.2 Adams—Moulton Method
6.2.3 Predictor—Corrector Methods
6.3 Global Description of Multistep Methods
6.3.1 Linear Difference Equations
6.32 Stability and Root Condition
6.3.3 Convergence
6.3.4 Asymptotics of Global Error
6.3.5 Estimation of Global Error
6.4 Analytic Theory of Orderand Stability
6.4.1 Analytic Characterization of Order
6.4.2 Stable Methods of Maximum Order
6.4.3 Applications
6.5 Stiff Problems
6.5.1 A—Stability
6.5.2 A（@）—Stability
6.6 Notesto Chapter6
Exercises and Machine Assignments to Chapter6
Exercises
Machine Assignments
Selected Solutions to Exercises
Selected Solutions to Machine Assignments
……
7 Two—Point Boundary Value Problems for ODEs
References
