Ecosyste.ms: Awesome
An open API service indexing awesome lists of open source software.
https://github.com/iydon/numericalanalysisnotes
Numerical Analysis Notes and Codes.
https://github.com/iydon/numericalanalysisnotes
latex-document numerical-analysis sustex
Last synced: 3 months ago
JSON representation
Numerical Analysis Notes and Codes.
- Host: GitHub
- URL: https://github.com/iydon/numericalanalysisnotes
- Owner: iydon
- License: mit
- Created: 2018-09-04T14:36:41.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2021-07-09T11:23:13.000Z (over 3 years ago)
- Last Synced: 2024-10-11T21:41:30.438Z (3 months ago)
- Topics: latex-document, numerical-analysis, sustex
- Language: Python
- Size: 2.8 MB
- Stars: 6
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Numerical_Analysis_Notes
Numerical Analysis Notes and Codes. XeLaTeX to compile. (option: '-shell-escape')
# Chapter 1: Mathematical Preliminaries and Error Analysis
- [ ] 1.1: Review of Calculus
- [x] 1.2: Round-off Errors and Computer Arithmetic
- [x] 1.3: Algorithms and Convergence
- [ ] 1.4: Numerical Software
# Chapter 2: Solutions of Equations in One Variable
- [x] 2.1 The Bisection Method
- [x] 2.2 Fixed-Point Iteration
- [x] 2.3 Newton's Method and Its Extensions
- [x] 2.4 Error Analysis for Iterative Methods
- [ ] 2.5 Accelerating Convergence
- [ ] 2.6 Zeros of Polynomials and Müller's Method
- [ ] 2.7 Survey of Methods and Software
# Chapter 3: Interpolation and Polynomial Approximation
- [x] 3.1 Interpolation and the Lagrange Polynomial
- [x] 3.2 Data Approximation and Neville's Method
- [x] 3.3 Divided Differences
- [x] 3.4 Hermite Interpolation
- [x] 3.5 Cubic Spline Interpolation
- [ ] 3.6 Parametric Curves
- [ ] 3.7 Survey of Methods and Software
# Chapter 4: Numerical Differentiation and Integration
- [x] 4.1 Numerical Differentiation
- [x] 4.2 Richardson's Extrapolation
- [x] 4.3 Elements of Numerical Integration
- [x] 4.4 Composite Numerical Integration
- [x] 4.5 Romberg Integration
- [ ] 4.6 Adaptive Quadrature Methods
- [x] 4.7 Gaussian Quadrature
- [ ] 4.8 Multiple Integrals
- [ ] 4.9 Improper Integrals
- [ ] 4.10 Survey of Methods and Software
# Chapter 5: Initial-Value Problems for Ordinary Differential Equations
- [x] 5.1 The Elementary Theory of Initial-Value Problems
- [x] 5.2 Euler’s Method
- [x] 5.3 Higher-Order Taylor Methods
- [x] 5.4 Runge-Kutta Methods
- [x] 5.5 Error Control and the Runge-Kutta-Fehlberg Method
- [x] 5.6 Multistep Methods
- [ ] 5.7 Variable Step-Size Multistep Methods
- [ ] 5.8 Extrapolation Methods
- [ ] 5.9 Higher-Order Equations and Systems of Differential Equations
- [ ] 5.10 Stability
- [ ] 5.11 Stiff Differential Equations
- [ ] 5.12 Survey of Methods and Software
# Chapter 6: Direct Methods for Solving Linear Systems
- [x] 6.1 Linear Systems of Equations
- [x] 6.2 Pivoting Strategies
- [ ] 6.3 Linear Algebra and Matrix Inversion
- [ ] 6.4 The Determinant of a Matrix
- [x] 6.5 Matrix Factorization
- [ ] 6.6 Special Types of Matrices
- [ ] 6.7 Survey of Methods and Software
# Chapter 7: IterativeTechniques in Matrix Algebra
- [x] 7.1 Norms of Vectors and Matrices
- [x] 7.2 Eigenvalues and Eigenvectors
- [x] 7.3 The Jacobi and Gauss-Siedel Iterative Techniques
- [ ] 7.4 Relaxation Techniques for Solving Linear Systems
- [x] 7.5 Error Bounds and Iterative Refinement
- [ ] 7.6 The Conjugate Gradient Method
- [ ] 7.7 Survey of Methods and Software
# Chapter 8: ApproximationTheory
- [ ] 8.1 Discrete Least Squares Approximation
- [ ] 8.2 Orthogonal Polynomials and Least Squares Approximation
- [ ] 8.3 Chebyshev Polynomials and Economization of Power Series
- [ ] 8.4 Rational Function Approximation
- [ ] 8.5 Trigonometric Polynomial Approximation
- [ ] 8.6 Fast Fourier Transforms
- [ ] 8.7 Survey of Methods and Software
# Chapter 9: Approximating Eigenvalues
- [ ] 9.1 Linear Algebra and Eigenvalues
- [ ] 9.2 Orthogonal Matrices and Similarity Transformations
- [ ] 9.3 The Power Method
- [ ] 9.4 Householder’s Method
- [ ] 9.5 The QR Algorithm
- [ ] 9.6 Singular Value Decomposition
- [ ] 9.7 Survey of Methods and Software
# Chapter 10: Numerical Solutions of Nonlinear Systems of Equations
- [ ] 10.1 Fixed Points for Functions of Several Variables
- [ ] 10.2 Newton’s Method
- [ ] 10.3 Quasi-Newton Methods
- [ ] 10.4 Steepest Descent Techniques
- [ ] 10.5 Homotopy and Continuation Methods
- [ ] 10.6 Survey of Methods and Software
# Chapter 11: Boundary-Value Problems for Ordinary Differential Equations
- [ ] 11.1 The Linear Shooting Method
- [ ] 11.2 The Shooting Method for Nonlinear Problems
- [ ] 11.3 Finite-Difference Methods for Linear Problems
- [ ] 11.4 Finite-Difference Methods for Nonlinear Problems
- [ ] 11.5 The Rayleigh-Ritz Method
- [ ] 11.6 Survey of Methods and Software