Overview
Reference: Richard L. Burden, J. Douglas Faires, Annette M. Burden, Numerical Analysis, 10th Edition, 2016.
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Course Coverage
Those chosen are homework coverage.
- Chapter 1: Mathematical Preliminaries
- 1.2 Roundoff Errors and Computer Arithmetic
- 1.3 Algorithms and Convergence
- Chapter 2, 6, 7, 5
- Chapter 2: Solutions of Equations in One Variable
- 2.1 The Bisection Method
- 2.2 Fixed-Point Iteration
- 2.3 Newton's Method
- 2.4 Error Analysis for Iterative Methods
- 2.5 Accelerating Convergence
- Chapter 6: Direct Methods for Solving Linear Systems
- 6.1 Linear Systems of Equations
- 6.2 Pivoting Strategies
- 6.5 Matrix Factorization
- 6.6 Special Types of Matrices
- Chapter 7: Iterative Techniques in Matrix Algebra
- 7.1 Norms of Vxectors and Matrices
- 7.2 Eigenvalues and Eigenvectors
- 7.3 The Jacobi and Gauss-Seidel Iterative Techniques
- 7.4 Relaxation Techniques for Solving Linear Systems
- 7.5 Error Bounds and Iterative Refinement
- Chapter 5: Initial-Value Problems for Ordinary Differential Equations
- 5.1 The Elementary Theory of Initial-Value Problems
- 5.2 Euler's Method
- 5.3 Higher-Order Taylor Methods
- 5.4 Runge-Kutta Methods
- 5.5 Error Control and the Runge-Kutta-Fehlberg Method
- 5.6 Multistep Methods
- 5.9 Higher-Order Equations and Systems of Differential Equations
- 5.10 Stability
- Chapter 2: Solutions of Equations in One Variable
- Chapter 3, 9, 8, 4
- Chapter 9: Approximating Eigenvalues
- 9.2 The Power Methods
- Chapter 3: Interpolation and Polynomial Approximation
- 3.1 Interpolation and the Lagrange Polynomial
- 3.2 Data Approximation and Neville's Method
- 3.3 Divided Differences
- 3.4 Hermite Interpolation
- 3.5 Cubic Spline Interpolation
- Chapter 8: Approximation Theory
- 8.1 Discrete Least Squares Approximation
- 8.2 Orthogonal Polynomials and Least Squares Approximation
- 8.3 Chebyshev Polynomials and Economization of Power Series
- Chapter 4: Numerical Differentiation and Integration
- 4.1 Numerical Differentiation
- 4.3 Elements of Numerical Integration
- 4.4 Composite Numerical Integration
- 4.5 Romberg Integration
- 4.2 Richardson's Extrapolation
- 4.6 Adaptive Quadrature Methods
- 4.7 Gaussian Quadrature
- Chapter 9: Approximating Eigenvalues