jack810914/numerical-analysis-examples

Numerical Analysis Implementations in Various Languages

Numerical Analysis Examples

Note: You can implement in any language for contribute.

1 Equation Solutions

1.1 Iteration Methods

• Bisection Method [[ C ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C/bisection/bisection.c) [ C++ ] [ C# ] [ Python ] [ Ruby ] [ Go ] [ Haskell ] [[ Racket ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Racket%20(Scheme)%20/bisection.rkt)
• Newton Method [[ C ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C/newtons-method/newtons-method.c) [ C++ ] [ C# ] [ Python ] [ Ruby ] [ Go ] [ Haskell ] [[ Racket ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Racket%20(Scheme)%20/newtons-method.rkt)
• Maximum Field Form [ C# ] [ Python ] [ Ruby ]
• Secant Method [[ C++ ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%2B%2B/secant/secant.cpp) [ C# ] [ Python ] [ Ruby ] [ Go ] [ Haskell ]
• Regula-Falsi Method [ C# ] [ Python ] [ Ruby ]
• Fixed-Point Method

2 Polynomials and Roots

2.1 Polynomial Roots

• Synthetic Division and Newton Method
• Muller Method

3 Linear Equations

3.1 Numerical Solutions of Equations

• Cramer Method
• Gaussian Elimination Method [ C# ]
• Gaussian-Jordan Method
• LU Decomposition Method [ C# ]

4 Matrix Operations

4.1 Basic Matrix Operations

• Addition, Subtraction, Multiplication, Transpose, Determinant [ C# ] [ Go ]

4.2 Determinant

• Determinant with Gaussian-Jordan Method
• Determinant with LU Decomposition Method

4.3 Matrix Inversion

• Inverse Matrix with Cramer's Rule [ C# ]
• Inverse Matrix with Gaussian Elimination Method [ C# ]
• Inverse Matrix with LU Decomposition

5 Eigenvalues and Eigenvectors

5.1 Finding Eigenvalues Methods

• Jacobian Transformation
• The QR and QL Algorithms

6 Linear Curve Fitting

6.1 Least Squares Method

• Example [[ Python ]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/leastsquares.py)

6.2 Polynomial Fitting

• Example

7 Nonlinear Curve Fitting

7.1 Algorithm

• Example

8 Fourier Series and Fourier Transform

8.1 Fourier Series

• Fourier Series Algorithm

8.2 Fourier Transform

• Fourier Sine and Cosine Transformation

8.3 Numerical Fourier Transform

• Discrete Fourier Transform
• Fast Fourier Transform

9 Interpolation

9.1 Lagrange Polynomial Interpolation

• Lagrange Interpolation Algorithm [ Haskell ] [ Python ]
• Neville Interpolation Algorithm

9.2 Cubic Spline Interpolation

• Cubic Spline Algorithm [ Haskell ]

9.3 Trigonometric Interpolation

• Example

9.4 Extrapolation

• Example

10 Derivative and Integral

10.1 Derivative

• Derivative of Sequences
• Point Derivative of Sequences

10.2 Numerical Integral

• Integration of Series
• Integration of Functions

11 Data Processing

11.1 Data Arrays and Digital Filters

• Average Filter
• Median Filter
• Fourier Transform and Filter Windows
• Savitzky Golay Filter

11.2 Spectral Decomposition

• Simulation and Curve Fitting
• Spectral Decomposition with Derivative
• Fourier Transform and Spectral Decomposition

12 Polynomial Calculus

• Example [[Python]] (https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/polynomial_calculus.py)

Contributing

1. Fork it ( https://github.com/ergenekonyigit/Numerical-Analysis-Examples/fork )
2. Create your feature branch (git checkout -b my-new-feature)
3. Commit your changes (git commit -am 'Add some feature')
4. Push to the branch (git push origin my-new-feature)
5. Create a new Pull Request

Contributors

• ergenekonyigit - creator, maintainer