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Numerical Analysis Examples

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Note: You can implement in any language for contribute.

1 Equation Solutions

1.1 Iteration Methods

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

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

9.2 Cubic Spline Interpolation

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

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