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Numerical-Analysis-Examples

★ 391 Open GitHub ↗

Numerical Analysis Implementations in Various Languages

// repository documentation

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# Numerical Analysis Examples
![cover](http://i.imgur.com/TXXVcwd.jpg)

Note: You can implement in any language for contribute.
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### 1 Equation Solutions
#### 1.1 Iteration Methods
* Bisection Method [[ C ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C/bisection/bisection.c) [[ C++ ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%2B%2B/bisectionmethod.cpp) [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/BisectionMethod/bisectionmethod.cs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/bisectionmethod.py) [[ Ruby ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Ruby/bisectionmethod.rb) [[ Go ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Go/bisectionmethod.go) [[ Haskell ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Haskell/BisectionMethod.hs) [[ 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++ ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%2B%2B/newtons-method/newtons-method.cpp) [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/NewtonMethod/newtonmethod.cs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/newtonmethod.py) [[ Ruby ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Ruby/newtonmethod.rb) [[ Go ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Go/newtonmethod.go) [[ Haskell ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Haskell/NewtonsMethod.hs) [[ Racket ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Racket%20(Scheme)%20/newtons-method.rkt)
 * Maximum Field Form [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/MaximumFieldForm/maximumfieldform.cs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/maximumfieldform.py) [[ Ruby ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Ruby/maximumfieldform.rb)
* Secant Method [[ C++ ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%2B%2B/secant/secant.cpp) [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/SecantMethod/secantmethod.cs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/secantmethod.py) [[ Ruby ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Ruby/secantmethod.rb) [[ Go ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Go/secantmethod.go) [[ Haskell ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Haskell/SecantMethod.hs)
* Regula-Falsi Method [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/RegulaFalsiMethod/regulafalsimethod.cs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/regulafalsimethod.py) [[ Ruby ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Ruby/regulafalsimethod.rb)
* 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# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/GaussianEliminationMethod/gaussianeliminationmethod.cs)
* Gaussian-Jordan Method
* LU Decomposition Method [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/tree/master/C%23/LUDecompositionMethod)

### 4 Matrix Operations
#### 4.1 Basic Matrix Operations
* Addition, Subtraction, Multiplication, Transpose, Determinant [[ C#  ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/tree/master/C%23/BasicMatrixOperations) [[ Go  ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Go/matrixoperations.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# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/C%23/InverseMatrixwithCramersRule/inversematrixcramersrule.cs)
* Inverse Matrix with Gaussian Elimination Method [[ C# ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/tree/master/C%23/InverseMatrixwithGaussianEliminationMethod)
* 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 ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Haskell/LagrangeInterpolation.hs) [[ Python ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Python/lagrangeinterpolation.py)
* Neville Interpolation Algorithm

#### 9.2 Cubic Spline Interpolation
* Cubic Spline Algorithm [[ Haskell ]](https://github.com/ergenekonyigit/Numerical-Analysis-Examples/blob/master/Haskell/SplineInterpolation.hs)

#### 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](https://github.com/ergenekonyigit) - creator, maintainer

Numerical-Analysis-Examples

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